Finite Group Databasebeta

← #14656919

Subgroups — #14656919

Order 2816.

508 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 95 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#13073628C211yesmaximal, characteristic, complemented
2#13069453C211yesmaximal, characteristic
3C2×#10622175C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic, complemented
5#13066483C211yesmaximal, characteristic, complemented
6#13066463C211yesmaximal, characteristic, complemented
7C11×#1519C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×#66931—21no—
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C2×#66898—21no—
13C2×#66898—21no—
14#10622825C2211yescharacteristic
15C4×C22⋊Dic11C2211yescharacteristic
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622597—21no—
19#10622592—21no—
20#10622559—21no—
21#10622260—21no—
22#10622259—21no—
23C11×#327—21no—
24C11×#327—21no—
25#10622175—21no—
26#10622175—21no—
27C22×D4×C11—21no—
28C22×D4×C11Q811yescharacteristic, complemented
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C22×Dic22—21no—
32C22×C8×C11—21no—
33C11×#121—21no—
34C11×#121—21no—
35C11×#121—21no—
36C11×#121—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4Q811yescharacteristic, complemented
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11D411yescharacteristic
43C2×C22⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C22×C11⋊C8—21no—
52#66931—42no—
53#66931—42no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58#66898—42no—
59#66898—42no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95D411yescharacteristic
66C11⋊#95D411yescharacteristic
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#10374—111nomaximal, Sylow
70C24×C11—21no—
71C24×C11C2×D411yescharacteristic
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—81no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—81no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×Q811yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—42no—
96C22×Dic11—41no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99C22×Dic11—81no—
100C2×Dic22—42no—
101C2×Dic22—42no—
102C2×Dic22—81no—
103C2×C8×C11—41no—
104C2×C8×C11—81no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—81no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C22⋊Dic11—21no—
113C22⋊Dic11—21no—
114C22⋊Dic11—41no—
115C22⋊Dic11—41no—
116C22⋊Dic11D812yes—
117C22⋊Dic11SD1612yes—
118C4⋊Dic11—42no—
119C4⋊Dic11—81no—
120Dic11⋊C4—42no—
121Dic11⋊C4—42no—
122Dic11⋊C4—42no—
123Dic11⋊C4—81no—
124C4×Dic11—81no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—81no—
127#2549—111no—
128#1964—111no—
129#1519D1111yescharacteristic
130C2×#327—111no—
131#1294—111no—
132#1289—111no—
133#1282—111no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—81no—
140C23×C11—81no—
141C23×C11#12011yescharacteristic
142C23×C11C22⋊Q811yescharacteristic
143C23×C11#12411yescharacteristic
144C23×C11C2×D811yescharacteristic
145C23×C11C2×SD1611yescharacteristic
146C23×C11AGL(1,ℤ/8)11yescharacteristic
147C23×C11#13711yescharacteristic
148D4×C11—81no—
149D4×C11—81no—
150D4×C11—81no—
151D4×C11—81no—
152D4×C11—81no—
153D4×C11—81no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
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×C11C22⋊Q811yescharacteristic
170C2×C4×C11C22⋊Q811yescharacteristic
171C2×C4×C11#12411yescharacteristic
172C2×C4×C11#12411yescharacteristic
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—82no—
186C2×Dic11—82no—
187C2×Dic11—81no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190Dic22—84no—
191C8×C11—81no—
192C11⋊C8—81no—
193C2×C22⋊Q8—221no—
194C2×#121C2×D1111yescharacteristic
195C2×#99—221no—
196C2×#99—221no—
197C2×C22⋊C8—111no—
198C2×C22⋊C8C2×D1111yescharacteristic
199#398—221no—
200#395—221no—
201#391—221no—
202#389—221no—
203#385—221no—
204#380—111no—
205#380C2×D1111yescharacteristic
206C4×C22⋊C4—111no—
207C2×#95—111no—
208#327—21no—
209#327—21no—
210#327—221no—
211#327—221no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—161no—
226C22×C11—161no—
227C22×C11#39311yescharacteristic
228C22×C11#44711yescharacteristic
229C22×C11#44811yescharacteristic
230C22×C11#47411yescharacteristic
231C22×C11#47611yescharacteristic
232C22×C11#48611yescharacteristic
233C22×C11#48911yescharacteristic
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11—81no—
241Dic11—42no—
242Dic11—42no—
243Dic11—42no—
244Dic11—81no—
245Dic11—161no—
246C22×Q8—221no—
247C22×D4—21no—
248C22×D4Dic2211yescharacteristic, complemented
249C23×C4—221no—
250C23×C4C22×D1111yescharacteristic
251C22×C8—21no—
252C22×C8—221no—
253C22⋊Q8—442no—
254C22⋊Q8—442no—
255#121—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4Dic2211yescharacteristic, complemented
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—221no—
272C2×C42—221no—
273#99—442no—
274#99—442no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279#95—111no—
280#95—111no—
281#95—221no—
282#95—221no—
283#95—221no—
284#95—221no—
285#95—221no—
286#95C22⋊D1111yescharacteristic
287#95C22⋊D1111yescharacteristic
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—161no—
295C2×C11#202311yescharacteristic
296C2×C11#203111yescharacteristic
297C2×C11#203211yescharacteristic
298C24—21no—
299C24D4×D1111yescharacteristic
300C2×Q8—442no—
301C2×Q8—442no—
302C2×Q8—881no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—81no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—81no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—442no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4—881no—
325C22×C4C2×Dic2211yescharacteristic
326C22×C4#433911yescharacteristic
327C22×C4D4×D1111yescharacteristic
328C22×C4#434111yescharacteristic
329C22×C4#434111yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331C2×C8—41no—
332C2×C8—81no—
333C2×C8—441no—
334C2×C8—881no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—81no—
338C4⋊C4—442no—
339C4⋊C4—442no—
340C4⋊C4—442no—
341C4⋊C4—442no—
342C4⋊C4—881no—
343C4⋊C4—881no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—112no—
349C22⋊C4—112no—
350C22⋊C4—221no—
351C22⋊C4—221no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C42—881no—
355C11#1037411yescharacteristic, complemented, Sylow
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—81no—
362C23—81no—
363C23#6693111yescharacteristic
364C23#6693811yescharacteristic
365C23D8×D1111yescharacteristic
366C23#6696411yescharacteristic
367C23SD16×D1111yescharacteristic
368C23#6696811yescharacteristic
369C23#6699011yescharacteristic
370Q8—884no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—882no—
405C2×C4—882no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4—881no—
409C2×C4#6693111yescharacteristic
410C2×C4#6693811yescharacteristic
411C2×C4#6697711yescharacteristic
412C2×C4#6698911yescharacteristic
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—81no—
426C22—81no—
427C22—81no—
428C22—161no—
429C22—161no—
430C22#1062237211yescharacteristic
431C22#1062237311yescharacteristic
432C22#1062237411yescharacteristic
433C22#1062237811yescharacteristic
434C22#1062256011yescharacteristic
435C22#1062276911yescharacteristic
436C22#1062278311yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—442no—
445C4—442no—
446C4—442no—
447C4—881no—
448C4—1761no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—161no—
456C2#1306975011yescharacteristic
457C2#1306978611yescharacteristic
458C2#1306979311yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1519C2
socleC22×C11#393
prime radicalC2×C11×#121C22
hypercenter#1519D11
hypocenterC11#10374
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
1. #13073628C2semidirect
4. #13066496C2semidirect
5. #13066483C2semidirect
6. #13066463C2semidirect
28. C22×D4×C11Q8semidirect
38. C2×C11×C4⋊C4Q8semidirect
248. C22×D4Dic22semidirect
266. C2×C4⋊C4Dic22semidirect
355. C11#10374semidirect

Maximal subgroups

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

subgroupindex
#130736282
#130694532
C2×#106221752
#130664962
#130664832
#130664632
C11×#15192
#1037411