Finite Group Databasebeta

← #14658196

Subgroups — #14658196

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074586C211yesmaximal, characteristic
2#13068809C211yesmaximal, characteristic
3#13068804C211yesmaximal, characteristic
4#13066495C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066459C211yesmaximal, characteristic
7C11×#1442C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×C11×#95—21no—
10C2×C11×#95—21no—
11C2×C11×#95C2211yescharacteristic
12C2×C11×#95C2211yescharacteristic
13#10622825C2211yescharacteristic
14#10622825C2211yescharacteristic
15#10622823—21no—
16#10622823—21no—
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66872—21no—
20C2×#66871—21no—
21#10622273—21no—
22#10622273—21no—
23#10622270—21no—
24#10622270—21no—
25#10622167—21no—
26#10622167—21no—
27C23×C4×C11—21no—
28C23×C4×C11—21no—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—42no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—42no—
51C11×#95—42no—
52C11×#95Q812yes—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)Q812yes—
62C22⋊(C11⋊C8)Q812yes—
63#66872—42no—
64#66871—42no—
65#10571—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×Q811yescharacteristic
96C22×C4×C11C2×Q811yescharacteristic
97C22×C4×C11C2×Q811yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—81no—
116Dic11⋊C4—81no—
117Dic11⋊C4—81no—
118Dic11⋊C4—81no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125#2646—111no—
126#1853—111no—
127#1852—111no—
128#1442D1111yescharacteristic
129#1294—111no—
130#1294—111no—
131#1280—111no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11#12011yescharacteristic
137C23×C11C22⋊Q811yescharacteristic
138C23×C11C4⋊Q811yescharacteristic
139C23×C11#13511yescharacteristic
140C23×C11#13511yescharacteristic
141C23×C11AGL(1,ℤ/8)11yescharacteristic
142C23×C11#13711yescharacteristic
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11C22⋊Q811yescharacteristic
176C2×C4×C11C22⋊Q811yescharacteristic
177C2×C4×C11C4⋊Q811yescharacteristic
178C2×C4×C11C4⋊Q811yescharacteristic
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C22×C4⋊C4C2×D1111yescharacteristic
194C2×#107—221no—
195C2×#106—221no—
196C2×C22⋊C8—111no—
197C2×C22⋊C8—111no—
198#400—221no—
199#400—221no—
200#398—221no—
201#398—221no—
202#385—221no—
203#385—221no—
204#380—111no—
205#380—111no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95C2×D1111yescharacteristic
209C2×#95C2×D1111yescharacteristic
210#340—221no—
211#340—221no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11#39511yescharacteristic
225C22×C11#44911yescharacteristic
226C22×C11#45211yescharacteristic
227C22×C11#45411yescharacteristic
228C22×C11#45511yescharacteristic
229C22×C11B(4,𝔽2)11yescharacteristic
230C22×C11#45811yescharacteristic
231C22×C11#47811yescharacteristic
232C22×C11#47911yescharacteristic
233C22×C11#49911yescharacteristic
234C22×C11#50111yescharacteristic
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—82no—
240C4×C11—82no—
241C4×C11—81no—
242C4×C11—81no—
243Dic11—81no—
244Dic11—81no—
245Dic11—81no—
246Dic11—81no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C22⋊D1111yescharacteristic
250C23×C4C22⋊D1111yescharacteristic
251C23×C4C22×D1111yescharacteristic
252C22×C8—221no—
253C22×C8—221no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267#107—442no—
268#106—442no—
269C22⋊C8—112no—
270C22⋊C8—112no—
271C22⋊C8—221no—
272C22⋊C8—221no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—42no—
277#95—42no—
278#95—221no—
279#95—221no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95—221no—
284#95Dic2212yes—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11#159711yescharacteristic
290C2×C11#160611yescharacteristic
291C2×C11#161211yescharacteristic
292C2×C11#161511yescharacteristic
293C2×C11#205911yescharacteristic
294C2×C11#206111yescharacteristic
295C2×C11#206211yescharacteristic
296C24C2×C22⋊D1111yescharacteristic
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4C2×Dic2211yescharacteristic
328C22×C4#433911yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4Q8×D1111yescharacteristic
332C22×C4Q8×D1111yescharacteristic
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—441no—
336C2×C8—441no—
337C2×C8—441no—
338C2×C8—441no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C4⋊C4—881no—
348C4⋊C4—881no—
349C4⋊C4—881no—
350C4⋊C4—881no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C11#1057111yescharacteristic, complemented, Sylow
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23#6697711yescharacteristic
361C23#6698511yescharacteristic
362C23#6699011yescharacteristic
363C23#6699511yescharacteristic
364C23#6699711yescharacteristic
365C23#6700311yescharacteristic
366C23#6700311yescharacteristic
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4#6694111yescharacteristic
412C2×C4#6694111yescharacteristic
413C2×C4#6694911yescharacteristic
414C2×C4#6694911yescharacteristic
415C8—442no—
416C8—442no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22#1062259211yescharacteristic
430C22#1062262211yescharacteristic
431C22#1062263511yescharacteristic
432C22#1062264511yescharacteristic
433C22#1062265011yescharacteristic
434C22#1062266011yescharacteristic
435C22#1062266611yescharacteristic
436C22#1062267411yescharacteristic
437C22#1062267511yescharacteristic
438C22#1062267711yescharacteristic
439C22#1062269311yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—82no—
445C4—82no—
446C4—81no—
447C4—81no—
448C4—881no—
449C4—881no—
450C4—881no—
451C4—881no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2#1306754311yescharacteristic
457C2#1306759411yescharacteristic
458C2#1306762811yescharacteristic
459C2#1306764511yescharacteristic
460C2#1306995411yescharacteristic
461C2#1306996611yescharacteristic
462C2#1306996911yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1442C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1442D11
hypocenterC11#10571
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1442

Complements

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

NH ≅ G/Ntype
355. C11#10571semidirect

Maximal subgroups

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

subgroupindex
#130745862
#130688092
#130688042
#130664952
#130664592
C11×#14422
#1057111