Finite Group Databasebeta

← #14649840

Subgroups — #14649840

Order 2816.

622 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 113 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#13074361C211yesmaximal, characteristic
2#13071233C211yesmaximal, characteristic, complemented
3#13067185C211yesmaximal, characteristic
4#13067183C211yesmaximal, characteristic
5C2×#10622107C211yesmaximal, characteristic, complemented
6#13066483C211yesmaximal, characteristic, complemented
7C11×#1289C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C2×#66939—21no—
11C2×#66930—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C11×#380C2211yescharacteristic
15#10622825C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622607—22no—
18#10622585—22no—
19#10622571—21no—
20#10622555—21no—
21#10622285C412yescomplemented
22#10622274C412yescomplemented
23#10622260—22no—
24#10622108—22no—
25#10622107—22no—
26#10622089—22no—
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11D411yescharacteristic
30C23×Dic11D411yescharacteristic
31C22×D44C2×C411yescharacteristic
32C22×C8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11—21no—
38#66983—21no—
39#66983—21no—
40#66983—21no—
41#66983—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4C2×C412yes—
55C2×Dic11⋊C4D412yes—
56C2×C4×Dic11—22no—
57C22×C11⋊C8—21no—
58#66939—42no—
59#66939—42no—
60#66930—42no—
61#66930—42no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×#95C2×C412yes—
65C11×#95D412yes—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C11⋊#95D412yes—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#9204—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C23×D11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—81no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—22no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—81no—
98C22×Dic11C22⋊C412yes—
99C22×Dic11C22⋊C412yes—
100C22×Dic11D812yes—
101C22×Dic11SD1612yes—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—81no—
105C2×C8×C11—41no—
106C2×C8×C11—81no—
107C11×C4⋊C4—81no—
108C11×C4⋊C4—81no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115(C2×D11)⋊C4—44no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—82no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—44no—
122C4⋊Dic11—81no—
123Dic11⋊C4—22no—
124Dic11⋊C4—22no—
125Dic11⋊C4—22no—
126Dic11⋊C4—22no—
127Dic11⋊C4—44no—
128Dic11⋊C4—82no—
129C4×Dic11—44no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—81no—
132#2618—111no—
133#2316—111no—
134#1519—111no—
135#1519—111no—
136C2×#324—111no—
137#1289—111no—
138#1289D1111yescharacteristic, complemented
139C23×C11—41no—
140C23×C11—41no—
141C23×C11C2×C22⋊C411yescharacteristic
142C23×C11#12011yescharacteristic
143C23×C11#12311yescharacteristic
144C23×C11C2×D811yescharacteristic
145C23×C11C2×SD1611yescharacteristic
146C23×C11AGL(1,ℤ/8)11yescharacteristic
147C23×C11#13711yescharacteristic
148C22×D11—42no—
149C22×D11—42no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11C4×D411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C22⋊D11—81no—
170C22⋊D11—81no—
171C22⋊D11—81no—
172C22⋊D11—81no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—81no—
189C2×Dic11#10214yes—
190D44—81no—
191D44—81no—
192C8×C11—81no—
193C11⋊C8—81no—
194C2×#123—221no—
195C2×#121—111no—
196C2×#117—221no—
197C22×C4⋊C4—111no—
198C2×C22⋊C8—111no—
199C2×C22⋊C8C2×D1111yescharacteristic
200#398—112no—
201#396—222no—
202#394—112no—
203#389—222no—
204#389—222no—
205#386—221no—
206#380—111no—
207#380—221no—
208#380C2×D1111yescharacteristic
209#380C2×D1111yescharacteristic
210#327—222no—
211#327—222no—
212#324—222no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11#38611yescharacteristic
224C22×C11C2×#10211yescharacteristic
225C22×C11#41711yescharacteristic
226C22×C11#44711yescharacteristic
227C22×C11#44811yescharacteristic
228C22×C11#48011yescharacteristic
229C22×C11#48111yescharacteristic
230C2×D11—82no—
231C2×D11—82no—
232C2×D11—81no—
233C2×D11—81no—
234C2×D11—81no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—82no—
240C4×C11—82no—
241Dic11—24no—
242Dic11—42no—
243Dic11—82no—
244Dic11—81no—
245C22×D4—111no—
246C22×D4—221no—
247C23×C4—111no—
248C23×C4—111no—
249C23×C4C22×D1111yescharacteristic
250C22×C8—21no—
251C22×C8—221no—
252#123—442no—
253#123—442no—
254#121—221no—
255#121—221no—
256#121—221no—
257#121—221no—
258#117—442no—
259#117—442no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—112no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4—222no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—221no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—222no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—221no—
278C2×C22⋊C4—222no—
279C2×C42—222no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—221no—
283C22⋊C8—221no—
284#95—112no—
285#95—222no—
286#95—222no—
287#95C4×D1112yes—
288#95D4412yes—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11#187411yescharacteristic
296C2×C11#191211yescharacteristic
297C2×C11#191311yescharacteristic
298D11—161no—
299C24—221no—
300C24D4×D1111yescharacteristic
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—881no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—81no—
313C22×C4—112no—
314C22×C4—112no—
315C22×C4—112no—
316C22×C4—112no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—222no—
325C22×C4—881no—
326C22×C4C2×C4×D1111yescharacteristic
327C22×C4C2×D4411yescharacteristic
328C22×C4#433911yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4#434311yescharacteristic
332C2×C8—41no—
333C2×C8—81no—
334C2×C8—441no—
335C2×C8—881no—
336C4⋊C4—81no—
337C4⋊C4—81no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—221no—
343C4⋊C4—221no—
344C4⋊C4—444no—
345C4⋊C4—444no—
346C4⋊C4—882no—
347C4⋊C4—881no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—444no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C22⋊C4—882no—
358C42—444no—
359C11#920411yescharacteristic, complemented, Sylow
360C23—41no—
361C23—41no—
362C23—442no—
363C23—442no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23C22⋊C4×D1111yescharacteristic
368C23#6693511yescharacteristic
369C23#6694711yescharacteristic
370C23D8×D1111yescharacteristic
371C23SD16×D1111yescharacteristic
372C23#6696711yescharacteristic
373C23#6697111yescharacteristic
374D4—881no—
375D4—881no—
376D4—881no—
377D4—881no—
378D4—881no—
379D4—881no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—114no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—442no—
407C2×C4—441no—
408C2×C4—881no—
409C2×C4C4×D4411yescharacteristic
410C2×C4#6693711yescharacteristic
411C2×C4#6694611yescharacteristic
412C2×C4#6694811yescharacteristic
413C8—81no—
414C8—881no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—882no—
426C22—882no—
427C22—881no—
428C22—881no—
429C22—881no—
430C22#1062227811yescharacteristic
431C22D11×#10211yescharacteristic
432C22#1062238611yescharacteristic
433C22#1062241611yescharacteristic
434C22#1062241911yescharacteristic
435C22#1062247611yescharacteristic
436C22#1062249511yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—82no—
443C4—224no—
444C4—442no—
445C4—882no—
446C4—881no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—1761no—
454C2#1306893211yescharacteristic
455C2#1306915211yescharacteristic
456C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1289C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1289D11
hypocenterC11#9204
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #13071233C2semidirect
5. C2×#10622107C2semidirect
6. #13066483C2semidirect
7. C11×#1289C2semidirect
21. #10622285C4semidirect
22. #10622274C4semidirect
138. #1289D11semidirect
359. C11#9204semidirect

Maximal subgroups

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

subgroupindex
#130743612
#130712332
#130671852
#130671832
C2×#106221072
#130664832
C11×#12892
#920411