Finite Group Databasebeta

← #14765291

Subgroups — #14765291

Order 2816.

796 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic
2C2×#10622732C211yesmaximal, characteristic, complemented
3#13071875C211yesmaximal, characteristic
4#13069338C212yesmaximal, complemented
5#13069226C212yesmaximal, complemented
6#13069178C212yesmaximal, complemented
7#13068799C211yesmaximal, characteristic, complemented
8#13068798C212yesmaximal, complemented
9#13068685C211yesmaximal, characteristic, complemented
10#13068395C211yesmaximal, characteristic, complemented
11C11×#1870C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C2×C11×C22⋊C8C2211yescharacteristic
18C2×C11×C22⋊C8C2212yes—
19#10622835C412yes—
20C4×C22⋊Dic11C2211yescharacteristic
21C4×C22⋊Dic11C2212yes—
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24#10622732—24no—
25C2×#66879C2212yes—
26C2×Dic11⋊C8C2212yes—
27C2×Dic11⋊C8C2212yes—
28C2×Dic11⋊C8C2212yes—
29#10622624—24no—
30#10622599C411yescharacteristic
31#10622596C411yescharacteristic
32#10622566C411yescharacteristic
33#10622565C412yes—
34#10622562C411yescharacteristic
35C4×Dic11⋊C4C2212yes—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×#66867C2211yescharacteristic
38C11×#336C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43C22×D4×C11C2×C411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C2×C11×M16—22no—
47C2×C11×M16—42no—
48C22×C8×C11C2312yes—
49C22×C8×C11C2312yes—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4C2×C411yescharacteristic
53C2×C11×C22⋊C4C2×C411yescharacteristic
54C2×C11×C22⋊C4C2×C411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11C2×C412yes—
57C2×C22⋊Dic11C2×C412yes—
58C2×C22⋊Dic11C2×C412yes—
59C2×C22⋊Dic11C2×C412yes—
60#66979—22no—
61#66979—22no—
62C2×C4⋊Dic11C2×C411yescharacteristic
63C2×C4⋊Dic11C2×C411yescharacteristic
64C2×Dic11⋊C4C2×C412yes—
65C2×Dic11⋊C4C2×C412yes—
66C2×C4×Dic11C2312yes—
67C2×C4×Dic11C2312yes—
68C2×#4318—22no—
69C2×#4318—42no—
70C22×C11⋊C8—42no—
71C22×C11⋊C8D414yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C11×C22⋊C8—22no—
77C11×C22⋊C8—42no—
78C11⋊#95C2×C412yes—
79C11⋊#95C2×C412yes—
80C11⋊#95C2×C411yescharacteristic
81C11⋊#95C2×C412yes—
82C11⋊#95C2×C412yes—
83C11⋊#95C2×C411yescharacteristic
84C22⋊(C11⋊C8)—22no—
85C22⋊(C11⋊C8)—22no—
86#66879—42no—
87Dic11⋊C8—24no—
88Dic11⋊C8—24no—
89Dic11⋊C8—42no—
90C4⋊(C11⋊C8)—22no—
91#66867—22no—
92#22070—111nomaximal, Sylow
93C24×C11C22×C411yescharacteristic
94C24×C11C22×C411yescharacteristic
95C2×D4×C11—22no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11C22×C412yes—
112C22×Dic11C22×C412yes—
113C22×Dic11C22×C412yes—
114C22×Dic11C22×C412yes—
115C11×M16—44no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C11×C4⋊C4—22no—
123C11×C22⋊C4—22no—
124C11×C22⋊C4—22no—
125C42×C11—21no—
126C42×C11—21no—
127C22⋊Dic11—24no—
128C22⋊Dic11—42no—
129C22⋊Dic11—42no—
130C22⋊Dic11—42no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133Dic11⋊C4—42no—
134Dic11⋊C4—42no—
135C4×Dic11—22no—
136C4×Dic11—22no—
137C4×Dic11—22no—
138C4×Dic11—22no—
139#4318—44no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—44no—
147C2×C11⋊C8C2×D412yes—
148C2×C11⋊C8C2×D412yes—
149C2×#435—111no—
150C2×#424—111no—
151#2395—111no—
152#1940—112no—
153#1924—112no—
154#1917—112no—
155#1870D1111yescharacteristic
156#1851—112no—
157#1851—111no—
158#1818—111no—
159#1752—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—22no—
166C23×C11—21no—
167C23×C11—22no—
168C23×C11—21no—
169C23×C11C4×D412yes—
170C23×C11C23×C411yescharacteristic
171D4×C11—44no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11C4×D412yes—
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11H(5,𝔽2)12yes—
190C2×C4×C112−1+412yes—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C8×C11—42no—
204C8×C11—42no—
205C11⋊C8—22no—
206C11⋊C8—22no—
207C11⋊C8—41no—
208C11⋊C8—41no—
209C22×M16—111no—
210C22×M16C2×D1111yescharacteristic
211C23×C8—111no—
212C2×C4×D4C2×D1111yescharacteristic
213C2×#117—111no—
214#435—224no—
215#424—224no—
216C2×C4⋊C8—112no—
217C2×C4⋊C8—112no—
218C2×C4⋊C8—111no—
219C2×C4⋊C8—112no—
220C2×C22⋊C8—111no—
221C2×C22⋊C8—111no—
222C2×C22⋊C8C2×D1111yescharacteristic
223C2×C22⋊C8C2×D1112yes—
224C2×#97—111no—
225C2×#97—112no—
226#400—111no—
227#399—111no—
228#398—111no—
229#397—112no—
230#397—111no—
231#394—112no—
232C4×C4⋊C4—112no—
233C4×C22⋊C4—112no—
234C4×C22⋊C4—111no—
235#336—112no—
236#336—112no—
237#336—112no—
238#336—112no—
239#336C2×D1112yes—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11C2×C4×D411yescharacteristic
251C22×C11#52012yes—
252C22×C11#56811yescharacteristic
253C22×C11#56811yescharacteristic
254C22×C11#56812yes—
255C4×C11—22no—
256C4×C11—41no—
257C4×C11—41no—
258C4×C11—41no—
259C4×C11#53411yescharacteristic
260C4×C11#53611yescharacteristic
261C4×C11#53912yes—
262Dic11—42no—
263Dic11—42no—
264Dic11—42no—
265Dic11—42no—
266C22×D4C4×D1111yescharacteristic
267C23×C4C22×D1111yescharacteristic
268C23×C4C22×D1111yescharacteristic
269C2×M16—22no—
270C2×M16—42no—
271C2×M16—222no—
272C2×M16—442no—
273C22×C8—111no—
274C22×C8—111no—
275C22×C8—114no—
276C22×C8—111no—
277C22×C8—111no—
278C22×C8—442no—
279C22×C8C22×D1112yes—
280C22×C8C22×D1112yes—
281C4×D4—22no—
282C4×D4—22no—
283#117—222no—
284#117—222no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4C4×D1111yescharacteristic
290C2×C22⋊C4—112no—
291C2×C22⋊C4—112no—
292C2×C22⋊C4—112no—
293C2×C22⋊C4—112no—
294C2×C22⋊C4C4×D1111yescharacteristic
295C2×C22⋊C4C4×D1111yescharacteristic
296C2×C42—112no—
297C2×C42—112no—
298C2×C42C22×D1111yescharacteristic
299C4⋊C8—222no—
300C4⋊C8—224no—
301C4⋊C8—224no—
302C4⋊C8—442no—
303C22⋊C8—22no—
304C22⋊C8—42no—
305C22⋊C8—222no—
306C22⋊C8—222no—
307#97—222no—
308#97—442no—
309#95—112no—
310#95—111no—
311#95—112no—
312#95—111no—
313#95—112no—
314#95—112no—
315C2×C11—42no—
316C2×C11—81no—
317C2×C11#232211yescharacteristic
318C2×C11#293011yescharacteristic
319C2×C11#293211yescharacteristic
320C2×C11#299512yes—
321C2×C11#299512yes—
322C24C2×C4×D1111yescharacteristic
323C24C2×C4×D1111yescharacteristic
324C2×D4—22no—
325C2×D4—41no—
326C2×D4—41no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—112no—
334C22×C4—112no—
335C22×C4—112no—
336C22×C4—112no—
337C22×C4C2×C4×D1111yescharacteristic
338C22×C4C2×C4×D1111yescharacteristic
339C22×C4C2×C4×D1111yescharacteristic
340C22×C4C2×C4×D1111yescharacteristic
341C22×C4D4×D1112yes—
342C22×C4#434112yes—
343C22×C4C23×D1111yescharacteristic
344M16—44no—
345M16—444no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—112no—
353C2×C8—112no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—221no—
357C2×C8—221no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—444no—
361C4⋊C4—22no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—442no—
365C4⋊C4—442no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—224no—
369C22⋊C4—442no—
370C22⋊C4—442no—
371C22⋊C4—442no—
372C42—21no—
373C42—21no—
374C42—222no—
375C42—222no—
376C42—222no—
377C42—222no—
378C11#2207011yescharacteristic, complemented, Sylow
379C23—21no—
380C23—21no—
381C23—22no—
382C23—22no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—22no—
387C23—22no—
388C23(C22⋊D11)⋊C412yes—
389C23C22×C4×D1111yescharacteristic
390D4—44no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4(C22⋊D11)⋊C412yes—
418C2×C4C2×D4×D1111yescharacteristic
419C2×C4C2×#434111yescharacteristic
420C2×C4#6703712yes—
421C2×C4#6704312yes—
422C8—42no—
423C8—42no—
424C8—222no—
425C8—222no—
426C8—441no—
427C8—441no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—42no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22C2×(C22⋊D11)⋊C411yescharacteristic
439C22#1062307712yes—
440C22#1062327611yescharacteristic
441C22#1062327611yescharacteristic
442C22#1062328112yes—
443C4—22no—
444C4—41no—
445C4—41no—
446C4—41no—
447C4—442no—
448C4—442no—
449C4—442no—
450C4—442no—
451C4#1062312011yescharacteristic
452C4#1062313312yes—
453C4#1062317911yescharacteristic
454C2—42no—
455C2—81no—
456C2#1307129011yescharacteristic
457C2#1307731511yescharacteristic
458C2#1307733111yescharacteristic
459C2#1307778012yes—
460C2#1307778212yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#22070
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#10622732C2semidirect
4. #13069338C2semidirect
5. #13069226C2semidirect
6. #13069178C2semidirect
7. #13068799C2semidirect
8. #13068798C2semidirect
9. #13068685C2semidirect
10. #13068395C2semidirect
378. C11#22070semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×#106227322
#130718752
#130693382
#130692262
#130691782
#130687992
#130687982
#130686852
#130683952
C11×#18702
#2207011