Finite Group Databasebeta

← #14658120

Subgroups — #14658120

Order 2816.

474 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 79 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#13079373C211yesmaximal, characteristic
2#13069082C211yesmaximal, characteristic, complemented
3#13069080C211yesmaximal, characteristic
4#13068801C211yesmaximal, characteristic, complemented
5#13067135C211yesmaximal, characteristic, complemented
6#13066492C211yesmaximal, characteristic, complemented
7C11×#1507C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C22×#4318C2211yescharacteristic
11C11×#407C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622831—21no—
14C2×#66897—21no—
15#10622820C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66888—21no—
18#10622654—21no—
19#10622654—21no—
20#10622653—21no—
21#10622647—21no—
22#10622584—21no—
23C2×C4⋊(C11⋊C8)—21no—
24C11×#327—21no—
25C11×#327—21no—
26#10622192—21no—
27#10622168—21no—
28#10622162—21no—
29#10622090—21no—
30#10622090—21no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×Dic22D411yescharacteristic
35C2×C11×M16—21no—
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C42×C11—21no—
44C2×C22⋊Dic11—21no—
45C2×#4324—21no—
46C2×#4324—21no—
47C2×C4⋊Dic11D411yescharacteristic
48#66977—21no—
49#66977—21no—
50#66977—21no—
51#66977—21no—
52C2×Dic11⋊C4—21no—
53C2×#4318—21no—
54C2×#4318—21no—
55C2×#4318—21no—
56C2×#4318—42no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8D411yescharacteristic
59C22×C11⋊C8D411yescharacteristic
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#95D411yescharacteristic
63C11×#95D411yescharacteristic
64#66897—42no—
65#66896—21no—
66#66896—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66888—42no—
72#66874—21no—
73#66874—21no—
74#66872—21no—
75#66872—21no—
76C4⋊(C11⋊C8)—42no—
77#10558—111nomaximal, Sylow
78C24×C11—21no—
79C24×C11#4111yescharacteristic
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—81no—
87C2×D4×C11—81no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×Dic11—21no—
100C22×Dic11—21no—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C11×M16—41no—
106C11×M16—41no—
107C2×C8×C11—41no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11—41no—
114C42×C11—41no—
115C22⋊Dic11—41no—
116C22⋊Dic11—41no—
117#4324—81no—
118#4324—81no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123#4318—22no—
124#4318—22no—
125#4318—41no—
126#4318—41no—
127#4318—41no—
128#4318—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137#3187—111no—
138#1901—111no—
139#1900—111no—
140#1851—111no—
141#1508—111no—
142#1507D1111yescharacteristic
143#1293—111no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11#12111yescharacteristic
153C23×C11#12311yescharacteristic
154C23×C11#12311yescharacteristic
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—81no—
158D4×C11—82no—
159D4×C11—81no—
160D4×C11—81no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—81no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12411yescharacteristic
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—81no—
186Dic22—41no—
187Dic22—41no—
188Dic22—81no—
189C8×C11—81no—
190C11⋊C8—42no—
191C11⋊C8—41no—
192C11⋊C8—41no—
193C11⋊C8—81no—
194C22×M16—111no—
195C2×C22⋊Q8—111no—
196C2×#121C2×D1111yescharacteristic
197#483—221no—
198#481—221no—
199#465—221no—
200#465—221no—
201#450—221no—
202#448—221no—
203C2×C4⋊C8—221no—
204C2×#101—221no—
205C2×#100—221no—
206#407—111no—
207#407C2×D1111yescharacteristic
208C2×C22⋊C8—111no—
209C4×C22⋊C4C2×D1111yescharacteristic
210#343—221no—
211#343—221no—
212#336—221no—
213#328—221no—
214#328—221no—
215#327—21no—
216#327—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—162no—
231C22×C11#39411yescharacteristic
232C22×C11#47111yescharacteristic
233C22×C11#47111yescharacteristic
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—42no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11B(4,𝔽2)11yescharacteristic
241C4×C11#45811yescharacteristic
242Dic11—81no—
243Dic11—81no—
244C22×Q8—111no—
245C22×D4—21no—
246C22×D4D4411yescharacteristic
247C23×C4C22×D1111yescharacteristic
248C2×SD16—221no—
249C2×SD16—221no—
250C2×M16—21no—
251C2×M16—221no—
252C2×M16—221no—
253C2×M16—221no—
254C2×M16—442no—
255C22×C8—111no—
256C22×C8—111no—
257C22×C8—221no—
258C22⋊Q8—221no—
259C22⋊Q8—221no—
260C22⋊Q8—221no—
261C22⋊Q8—221no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4D4411yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—221no—
272C2×C42—21no—
273#106—221no—
274#106—221no—
275C4⋊C8—442no—
276#103—221no—
277#103—221no—
278#102—221no—
279#102—221no—
280#101—442no—
281#100—442no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—221no—
285C22⋊C8—221no—
286C22⋊C8—221no—
287C22⋊C8—221no—
288#95C22⋊D1111yescharacteristic
289#95C22⋊D1111yescharacteristic
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—41no—
293C2×C11—41no—
294C2×C11—161no—
295C2×C11#204411yescharacteristic
296C2×C11#204611yescharacteristic
297C2×C11#205011yescharacteristic
298C24—21no—
299C24#434111yescharacteristic
300C2×Q8—221no—
301C2×Q8—221no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—81no—
311C2×D4—81no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4C2×D4411yescharacteristic
320C22×C4#433911yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325SD16—881no—
326SD16—881no—
327M16—41no—
328M16—41no—
329M16—222no—
330M16—222no—
331M16—441no—
332M16—441no—
333M16—441no—
334M16—441no—
335C2×C8—41no—
336C2×C8—222no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—441no—
340C2×C8—441no—
341C2×C8—441no—
342C2×C8—441no—
343C2×C8—441no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C22⋊C4—42no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C42—41no—
356C42—41no—
357C11#1055811yescharacteristic, complemented, Sylow
358C23—21no—
359C23—21no—
360C23—41no—
361C23—41no—
362C23—42no—
363C23—41no—
364C23—81no—
365C23—81no—
366C23#6693611yescharacteristic
367C23#6693911yescharacteristic
368C23#6699211yescharacteristic
369Q8—441no—
370Q8—441no—
371Q8—881no—
372D4—41no—
373D4—41no—
374D4—81no—
375D4—82no—
376D4—81no—
377D4—81no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—881no—
399C2×C4#6693511yescharacteristic
400C2×C4#6693811yescharacteristic
401C2×C4#6698311yescharacteristic
402C2×C4#6699111yescharacteristic
403C8—81no—
404C8—442no—
405C8—441no—
406C8—441no—
407C8—881no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—162no—
422C22#1062257411yescharacteristic
423C22#1062281311yescharacteristic
424C22#1062281311yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—42no—
429C4—81no—
430C4—81no—
431C4—881no—
432C4—881no—
433C4#1062235411yescharacteristic
434C4#1062235511yescharacteristic
435C2—21no—
436C2—21no—
437C2—41no—
438C2—41no—
439C2—161no—
440C2#1306986611yescharacteristic
441C2#1306987811yescharacteristic
442C2#1306990211yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1507C2
socleC22×C11#394
prime radicalC2×C11×#121C22
hypercenter#1507D11
hypocenterC11#10558
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #13069082C2semidirect
4. #13068801C2semidirect
5. #13067135C2semidirect
6. #13066492C2semidirect
357. C11#10558semidirect

Maximal subgroups

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

subgroupindex
#130793732
#130690822
#130690802
#130688012
#130671352
#130664922
C11×#15072
#1055811