Finite Group Databasebeta

← #14656138

Subgroups — #14656138

Order 2816.

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

normal subgroups only

This group has 610 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#13073612C211yesmaximal, characteristic, complemented
3#13067288C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic, complemented
5#13067006C211yesmaximal, characteristic, complemented
6#13066518C211yesmaximal, characteristic, complemented
7C11×#3226C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#67002—21no—
11C2×#67000—21no—
12C2×C4×D44C2211yescharacteristic
13C11×#500—21no—
14C11×#486—21no—
15C11×#480—22no—
16C11×#474—22no—
17C11×#431C2211yescharacteristic
18#10622845—21no—
19#10622843—21no—
20#10622696—21no—
21#10622685—21no—
22#10622670—22no—
23#10622606—22no—
24#10622600—22no—
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—
51#67000—42no—
52#67000—42no—
53C2×#4325—22no—
54C2×#4323—22no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D411yescharacteristic
59C2×C4×Dic11—21no—
60C2×#4318—21no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65C11×#107—24no—
66C11×C4⋊C8D412yes—
67C11×#102—24no—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70#66899—22no—
71#66896—22no—
72C11⋊#95—24no—
73C11⋊#95D412yes—
74C22⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78C4×C11⋊C8—21no—
79#10239—111nomaximal, Sylow
80C23×D11—21no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—22no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—22no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44D812yes—
109C2×C4×D11—44no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C8×C11—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125#4325—44no—
126#4323—44no—
127(C2×D11)⋊C4—48no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—42no—
133C4×Dic11—41no—
134C4×Dic11—41no—
135#4318—41no—
136#4318—41no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—41no—
139#3226D1111yescharacteristic, complemented
140#3036—111no—
141#2547—111no—
142#1546—111no—
143#1502—111no—
144#1478—111no—
145#1303—111no—
146C23×C11—41no—
147C23×C11#12011yescharacteristic
148C22×D11—22no—
149C22×D11—42no—
150C22×D11—42no—
151C22×D11—41no—
152C22×D11—41no—
153Q8×C11—41no—
154Q8×C11—41no—
155Q8×C11—81no—
156Q8×C11—81no—
157Q8×C11—81no—
158Q8×C11—81no—
159D4×C11—41no—
160D4×C11—41no—
161D4×C11—42no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11—81no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188D44—22no—
189D44—22no—
190D44—41no—
191D44—41no—
192C4×D11—82no—
193C4×D11—82no—
194C8×C11—42no—
195C11⋊C8—42no—
196C11⋊C8—81no—
197C2×AGL(1,ℤ/8)—221no—
198#532C2×D1111yescharacteristic
199C2×C4⋊Q8C2×D1111yescharacteristic
200C2×#124—221no—
201C2×C4×D4—111no—
202#500—21no—
203#486—21no—
204#480—22no—
205#474—22no—
206#463—222no—
207#461—221no—
208#459—221no—
209#431—111no—
210#431C2×D1111yescharacteristic
211#423—111no—
212#417—221no—
213#397—222no—
214#391—221no—
215#380—222no—
216C4×C4⋊C4—111no—
217#332—222no—
218#327—222no—
219D4⋊C8—222no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#39211yescharacteristic
226C22×C11#44711yescharacteristic
227C22×C11#44911yescharacteristic
228C2×D11—44no—
229C2×D11—42no—
230C2×D11—82no—
231C2×D11—81no—
232C2×D11—81no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—82no—
237C4×C11—81no—
238C4×C11#44711yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#45412yes—
241C4×C11#46611yescharacteristic
242C4×C11#46911yescharacteristic
243Dic11—82no—
244Dic11—81no—
245C2×#41—21no—
246C22×Q8—21no—
247C22×D4—111no—
248C23×C4—221no—
249AGL(1,ℤ/8)—442no—
250AGL(1,ℤ/8)—442no—
251C2×SD16—222no—
252C2×D8—222no—
253C2×M16—221no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8C22⋊D1111yescharacteristic
259#127C22⋊D1111yescharacteristic
260#124—21no—
261#124—442no—
262#124—442no—
263#121—21no—
264#121—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—221no—
268C4×D4—221no—
269C4×D4—221no—
270C4×D4—221no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4C22⋊D1112yes—
275C2×C22⋊C4—224no—
276C2×C22⋊C4—221no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279#107—24no—
280C4⋊C8—112no—
281C4⋊C8—221no—
282C4⋊C8—221no—
283C4⋊C8C22⋊D1112yes—
284#103—222no—
285#102—24no—
286#102—222no—
287C22⋊C8—21no—
288C22⋊C8—221no—
289C4×C8—21no—
290C4×C8—221no—
291#95—112no—
292#95—224no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—161no—
296C2×C11#199911yescharacteristic
297C2×C11#200311yescharacteristic
298C2×C11#200911yescharacteristic
299D11—82no—
300C24—221no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305C2×Q8—21no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—112no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—221no—
322C22×C4—22no—
323C22×C4—41no—
324C22×C4—222no—
325C22×C4—221no—
326C22×C4—444no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332SD16—444no—
333D8—444no—
334M16—441no—
335M16—441no—
336C2×C8—22no—
337C2×C8—222no—
338C2×C8—441no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—442no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—448no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C42—441no—
354C42—441no—
355C42D4×D1111yescharacteristic
356C42#434111yescharacteristic
357C42C2×C22⋊D1111yescharacteristic
358C42C2×C22⋊D1111yescharacteristic
359C11#1023911yescharacteristic, complemented, Sylow
360C23—41no—
361C23—222no—
362C23—442no—
363C23—442no—
364C23—441no—
365C23—441no—
366C23#6699011yescharacteristic
367Q8—41no—
368Q8—41no—
369Q8—81no—
370Q8—81no—
371Q8—81no—
372Q8—81no—
373D4—41no—
374D4—41no—
375D4—42no—
376D4—81no—
377D4—81no—
378D4—81no—
379D4—222no—
380D4—222no—
381D4—441no—
382D4—441no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—441no—
396C2×C4—882no—
397C2×C4—882no—
398C2×C4D8×D1111yescharacteristic
399C2×C4#6696411yescharacteristic
400C2×C4#6696411yescharacteristic
401C2×C4#6696511yescharacteristic
402C2×C4#6699011yescharacteristic
403C2×C4#6699111yescharacteristic
404C2×C4#6699211yescharacteristic
405C2×C4#6699211yescharacteristic
406C2×C4#6699311yescharacteristic
407C2×C4#6700611yescharacteristic
408C8—42no—
409C8—442no—
410C8—881no—
411C22—21no—
412C22—21no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—444no—
417C22—442no—
418C22—882no—
419C22—881no—
420C22—881no—
421C22#1062276911yescharacteristic
422C22#1062277111yescharacteristic
423C22#1062283611yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—82no—
428C4—81no—
429C4—882no—
430C4—881no—
431C4#1062276911yescharacteristic
432C4#1062277011yescharacteristic
433C4#1062277111yescharacteristic
434C4#1062277211yescharacteristic
435C4#1062285812yes—
436C2—21no—
437C2—21no—
438C2—161no—
439C2—882no—
440C2#1306961111yescharacteristic
441C2#1306963611yescharacteristic
442C2#1306967411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3226C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#3226D11
hypocenterC11#10239
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
2. #13073612C2semidirect
3. #13067288C2semidirect
4. #13067111C2semidirect
5. #13067006C2semidirect
6. #13066518C2semidirect
7. C11×#3226C2semidirect
139. #3226D11semidirect
359. C11#10239semidirect

Maximal subgroups

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

subgroupindex
#130780762
#130736122
#130672882
#130671112
#130670062
#130665182
C11×#32262
#1023911