Finite Group Databasebeta

← #14650352

Subgroups — #14650352

Order 2816.

564 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079374C211yesmaximal, characteristic
2#13071699C211yesmaximal, characteristic, complemented
3#13069452C211yesmaximal, characteristic
4#13067189C211yesmaximal, characteristic, complemented
5C2×#10622108C211yesmaximal, characteristic
6#13066496C211yesmaximal, characteristic, complemented
7C11×#1282C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622825C2211yescharacteristic
14C2×C11⋊#95C2211yescharacteristic
15#10622727—22no—
16C2×#66870—21no—
17C2×#66870—21no—
18#10622559—21no—
19C22⋊C4×Dic11—21no—
20#10622546—21no—
21C4×Dic11⋊C4—21no—
22#10622351—21no—
23#10622348—21no—
24#10622344C412yescomplemented
25#10622334C412yescomplemented
26#10622267—21no—
27#10622259—21no—
28#10622108—21no—
29#10622108—21no—
30#10622105—22no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C23×Dic11—21no—
34C22×D44C2×C411yescharacteristic
35C22×Dic22D411yescharacteristic
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43#66983—21no—
44#66983—21no—
45#66983—21no—
46#66983—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51#66977—21no—
52#66977—21no—
53#66977C2×C412yes—
54#66977D412yes—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11—21no—
59C2×C4×Dic11—21no—
60C2×#4314—22no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8C2×C412yes—
65C11×#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95D411yescharacteristic
73C11⋊#95D411yescharacteristic
74#66885—22no—
75#66881—22no—
76#66880—22no—
77#66870—42no—
78#66870—42no—
79#9278—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—81no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—42no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11—81no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—81no—
110C2×Dic22—21no—
111C2×Dic22—81no—
112C2×Dic22C22⋊C412yes—
113C2×C8×C11—22no—
114C2×C8×C11—41no—
115C2×C8×C11—81no—
116C2×C8×C11—81no—
117C11×C22⋊C4—21no—
118C11×C22⋊C4—21no—
119C11×C22⋊C4—21no—
120C11×C22⋊C4SD1612yescomplemented
121C42×C11—81no—
122C22⋊Dic11—22no—
123C22⋊Dic11—22no—
124C22⋊Dic11—41no—
125C22⋊Dic11—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—81no—
132C4⋊Dic11C22⋊C412yes—
133Dic11⋊C4—22no—
134Dic11⋊C4—22no—
135Dic11⋊C4—42no—
136Dic11⋊C4—81no—
137C4×Dic11—42no—
138C4×Dic11—81no—
139#4314—82no—
140#3187—111no—
141#2368—111no—
142#1964—111no—
143#1520—111no—
144C2×#327—111no—
145#1294—111no—
146#1282D1111yescharacteristic, complemented
147C23×C11—41no—
148C23×C11—41no—
149C23×C11C4×D411yescharacteristic
150C23×C11#12011yescharacteristic
151C23×C11#12111yescharacteristic
152C23×C11C2×SD1611yescharacteristic
153C23×C11#13511yescharacteristic
154C23×C11AGL(1,ℤ/8)11yescharacteristic
155C23×C11#13711yescharacteristic
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—81no—
160C22×D11—81no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11C2×C22⋊C411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12311yescharacteristic
177C22⋊D11—81no—
178C22⋊D11—81no—
179C22⋊D11—81no—
180C22⋊D11—81no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—82no—
197C2×Dic11—82no—
198C2×Dic11—81no—
199C2×Dic11—81no—
200C2×Dic11—81no—
201D44—42no—
202D44—81no—
203Dic22—42no—
204Dic22—81no—
205C8×C11—42no—
206C8×C11—81no—
207C2×C22⋊Q8—111no—
208C2×#121—111no—
209#483—112no—
210#481—221no—
211#465—222no—
212#450—112no—
213#448—221no—
214C2×#99—221no—
215C2×#99—221no—
216C2×C22⋊C8C2×D1111yescharacteristic
217C2×C22⋊C8C2×D1111yescharacteristic
218#391—221no—
219#387—221no—
220#387—221no—
221#385—221no—
222#380—111no—
223C4×C4⋊C4—221no—
224C4×C22⋊C4—221no—
225C4×C22⋊C4C2×D1111yescharacteristic
226C2×#95—111no—
227#328—222no—
228#327—221no—
229#327—221no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11#38611yescharacteristic
241C22×C11C4×SD1611yescharacteristic
242C22×C11#44011yescharacteristic
243C22×C11#44811yescharacteristic
244C22×C11#44911yescharacteristic
245C22×C11#46011yescharacteristic
246C22×C11#46411yescharacteristic
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—161no—
251C2×D11—161no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—42no—
257C4×C11—81no—
258Dic11—42no—
259Dic11—42no—
260Dic11—42no—
261Dic11—81no—
262Dic11—81no—
263Dic11—161no—
264C22×Q8—111no—
265C22×D4—111no—
266C22×D4—221no—
267C23×C4—221no—
268C23×C4C22×D1111yescharacteristic
269C2×SD16—222no—
270C22×C8—21no—
271C22×C8—21no—
272C22⋊Q8—112no—
273C22⋊Q8—112no—
274C22⋊Q8—221no—
275C22⋊Q8—221no—
276#121—221no—
277#121—221no—
278#121—221no—
279#121—221no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—221no—
289C2×C22⋊C4D4411yescharacteristic
290C2×C22⋊C4D4411yescharacteristic
291C2×C42—21no—
292C2×C42—221no—
293C2×C42—221no—
294#106—222no—
295#103—222no—
296#102—222no—
297#99—442no—
298#99—442no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8C4×D1112yes—
303#95—21no—
304#95—111no—
305#95—111no—
306#95—221no—
307#95—221no—
308#95—221no—
309#95—221no—
310#95—221no—
311#95—221no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11#188011yescharacteristic
319C2×C11#190611yescharacteristic
320C2×C11#191311yescharacteristic
321D11—161no—
322C24—221no—
323C24C2×D4411yescharacteristic
324C2×Q8—112no—
325C2×Q8—221no—
326C2×Q8—881no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—441no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—441no—
335C2×D4—881no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—81no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—442no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—881no—
349C22×C4C2×C4×D1111yescharacteristic
350C22×C4#433911yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4#434311yescharacteristic
355SD16—882no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—81no—
359C2×C8—81no—
360C4⋊C4—112no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—442no—
367C4⋊C4—881no—
368C4⋊C4—881no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—222no—
373C22⋊C4—222no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C22⋊C4#431412yescomplemented
379C42—81no—
380C42—442no—
381C42—881no—
382C11#927811yescharacteristic, complemented, Sylow
383C23—41no—
384C23—41no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23—881no—
389C23—881no—
390C23C4×D4411yescharacteristic
391C23#6693511yescharacteristic
392C23#6694811yescharacteristic
393C23C2×#431411yescharacteristic
394C23#6695711yescharacteristic
395C23#6696111yescharacteristic
396C23#6696211yescharacteristic
397Q8—442no—
398Q8—881no—
399D4—442no—
400D4—881no—
401D4—881no—
402D4—881no—
403D4—881no—
404D4—881no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—882no—
433C2×C4—882no—
434C2×C4—881no—
435C2×C4—881no—
436C2×C4—881no—
437C2×C4C22⋊C4×D1111yescharacteristic
438C2×C4#6693711yescharacteristic
439C2×C4#6694611yescharacteristic
440C2×C4#6694711yescharacteristic
441C8—42no—
442C8—81no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—881no—
454C22—881no—
455C22—881no—
456C22—1761no—
457C22—1761no—
458C22#1062227811yescharacteristic
459C22C4×#431411yescharacteristic
460C22#1062232311yescharacteristic
461C22#1062234711yescharacteristic
462C22#1062235111yescharacteristic
463C22#1062245811yescharacteristic
464C22#1062246111yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—81no—
471C4—442no—
472C4—442no—
473C4—442no—
474C4—881no—
475C4—881no—
476C4—1761no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2—21no—
483C2—1761no—
484C2#1306897011yescharacteristic
485C2#1306911811yescharacteristic
486C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1282C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1282D11
hypocenterC11#9278
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
2. #13071699C2semidirect
4. #13067189C2semidirect
6. #13066496C2semidirect
7. C11×#1282C2semidirect
24. #10622344C4semidirect
25. #10622334C4semidirect
120. C11×C22⋊C4SD16semidirect
146. #1282D11semidirect
378. C22⋊C4#4314semidirect
382. C11#9278semidirect

Maximal subgroups

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

subgroupindex
#130793742
#130716992
#130694522
#130671892
C2×#106221082
#130664962
C11×#12822
#927811