Finite Group Databasebeta

← #14782531

Subgroups — #14782531

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622385C212yesmaximal
2#13071103C211yesmaximal, characteristic
3#13071022C211yesmaximal, characteristic, complemented
4#13070036C211yesmaximal, characteristic, complemented
5#13070035C211yesmaximal, characteristic, complemented
6#13070029C211yesmaximal, characteristic, complemented
7#13070028C212yesmaximal, complemented
8#13070022C212yesmaximal, complemented
9#13068331C212yesmaximal, complemented
10D11×#336C211yesmaximal, characteristic, complemented
11C11×#2073C211yesmaximal, characteristic, complemented
12C22×#4341C2211yescharacteristic
13C22×C8×D11C2212yes—
14C2×#66945C2211yescharacteristic
15C2×#66945C2212yes—
16C2×C42×D11C2211yescharacteristic
17C2×C11×#102C2212yes—
18C11×#390C2211yescharacteristic
19C11×#382C2211yescharacteristic
20#10622834C2211yescharacteristic
21C2×#66896C2212yes—
22C2×#66880C2212yes—
23#10622589C2212yes—
24#10622587C2211yescharacteristic
25C2×#66874C2212yes—
26#10622569—22no—
27C22⋊C4×Dic11—22no—
28#10622549C2211yescharacteristic
29#10622542C2211yescharacteristic
30#10622385—28no—
31#10622280—22no—
32#10622262—22no—
33C11×#340C2212yes—
34C11×#336C2211yescharacteristic
35#10622189C2212yes—
36#10622188C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622162C2211yescharacteristic
40C22×D4×C11C2311yescharacteristic
41C22×C22⋊D11—21no—
42C23×Dic11—21no—
43C2×#4341—24no—
44C2×#4341—24no—
45C2×#4341—22no—
46C2×#4341D414yes—
47C22×C4×D11D412yes—
48C22×C4×D11C2311yescharacteristic
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2312yes—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C22⋊C4—22no—
54C2×C42×C11C2311yescharacteristic
55C2×C22⋊Dic11—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2312yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11D412yes—
65C2×C4×Dic11C2311yescharacteristic
66C22×C11⋊C8C2312yes—
67C2×C8×D11—24no—
68C2×C8×D11—24no—
69C2×C8×D11—24no—
70#66945—24no—
71#66945—24no—
72#66945—24no—
73C42×D11—24no—
74C11×#102—24no—
75C11×#95—22no—
76#66896—24no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80#66880—24no—
81#66874—24no—
82#23627—111nomaximal, Sylow
83C24×C11—21no—
84C23×D11C2×D411yescharacteristic
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11C2×D412yes—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2411yescharacteristic
93C2×C22⋊D11—24no—
94C2×C22⋊D11—42no—
95C2×C22⋊D11—42no—
96C22×Dic11—24no—
97C22×Dic11—21no—
98C22×Dic11—22no—
99C22×Dic11—21no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C22×Dic11C2×D412yes—
103C22×Dic11C2×D411yescharacteristic
104#4341—216no—
105#4341—48no—
106C2×C4×D11—24no—
107C2×C4×D11—24no—
108C2×C4×D11—42no—
109C2×C4×D11C2×D412yes—
110C2×C4×D11#4112yes—
111C2×C4×D11#4114yes—
112C2×C4×D11#4114yes—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22—21no—
116C2×Dic22C2×D412yes—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C22⋊C4—44no—
124C42×C11—22no—
125C22⋊Dic11—44no—
126(C2×D11)⋊C4—44no—
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131Dic11⋊C4—44no—
132Dic11⋊C4—44no—
133C4×Dic11—24no—
134C4×Dic11—22no—
135C4×Dic11—44no—
136C4×Dic11—42no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C8×D11—48no—
141C2×#416—112no—
142#2297—111no—
143#2285—111no—
144#2074—111no—
145#2074—111no—
146#2073—111no—
147#2073D1111yescharacteristic, complemented
148#2072—112no—
149#2071—112no—
150#1735—112no—
151C2×#336—111no—
152C23×C11—22no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11C22×D411yescharacteristic
158C22×D11—22no—
159C22×D11—22no—
160C22×D11#12112yes—
161C22×D11#12312yes—
162C22×D11#12412yes—
163D4×C11—24no—
164D4×C11—42no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4112yes—
175C2×C4×C11C2×#4112yes—
176C2×C4×C11C2×#4111yescharacteristic
177C22⋊D11—48no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—48no—
184C2×Dic11—42no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11#12112yes—
190C2×Dic11#12312yes—
191C2×Dic11#12412yes—
192C2×Dic11#13514yes—
193C4×D11—48no—
194C4×D11#12318yes—
195C4×D11#12618yes—
196Dic22—24no—
197Dic22—42no—
198C8×C11—42no—
199C11⋊C8—42no—
200C22×#41—111no—
201C23×C8—112no—
202C2×#117—112no—
203C2×#117—111no—
204C22×C42—111no—
205#416—228no—
206C2×#103—112no—
207C2×#103—112no—
208C2×#102—112no—
209C2×#102C2×D1112yes—
210#391—111no—
211#391—111no—
212#390—111no—
213#390C2×D1111yescharacteristic
214#386—222no—
215#384—112no—
216#382—111no—
217#382C2×D1111yescharacteristic
218#380—222no—
219C4×C4⋊C4—222no—
220C4×C22⋊C4—222no—
221#340—112no—
222#340—112no—
223#340—112no—
224#340C2×D1112yes—
225#336—112no—
226#336—111no—
227#336C2×D1111yescharacteristic
228C22×C11—42no—
229C22×C11—44no—
230C22×C11—82no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11C2×#12111yescharacteristic
234C22×C11C2×#12311yescharacteristic
235C22×C11C2×#12411yescharacteristic
236C22×C11C2×#13512yes—
237C22×C11#57512yes—
238C2×D11—24no—
239C2×D11—22no—
240C2×D11—22no—
241C2×D11—24no—
242C2×D11#39714yes—
243C4×C11—42no—
244C4×C11—81no—
245C4×C11—82no—
246C4×C11C2×#12312yes—
247C4×C11C2×#12612yes—
248Dic11—24no—
249Dic11—42no—
250Dic11—81no—
251Dic11—82no—
252Dic11#39714yes—
253C2×#41—114no—
254C2×#41—222no—
255C2×#41—224no—
256C2×#41—224no—
257C22×Q8—111no—
258C22×D4—221no—
259C22×D4C22×D1111yescharacteristic
260C23×C4—111no—
261C23×C4—112no—
262C23×C4—221no—
263C22×C8—112no—
264C22×C8—224no—
265C22×C8—224no—
266C22×C8—224no—
267C22×C8C22×D1112yes—
268#117—224no—
269#117—224no—
270#117—224no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4C22×D1111yescharacteristic
276C2×C4⋊C4C22×D1112yes—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—222no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—222no—
281C2×C42—112no—
282C2×C42—111no—
283C2×C42—224no—
284C2×C42—221no—
285C2×C42—222no—
286C2×C42C22×D1111yescharacteristic
287#103—224no—
288#103—224no—
289#102—24no—
290#102—224no—
291#95—22no—
292#95—222no—
293#95—222no—
294#95—222no—
295C2×C11—82no—
296C2×C11C2×#39711yescharacteristic
297C2×C11#303512yes—
298C2×C11#309112yes—
299C2×C11#313111yescharacteristic
300C2×C11#313511yescharacteristic
301D11—24no—
302C24—21no—
303C24—111no—
304#41—2216no—
305#41—448no—
306C2×Q8—112no—
307C2×Q8—221no—
308C2×Q8—222no—
309C2×Q8—222no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—224no—
314C2×D4—442no—
315C2×D4—442no—
316C2×D4D4×D1112yes—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—111no—
320C22×C4—112no—
321C22×C4—114no—
322C22×C4—112no—
323C22×C4—114no—
324C22×C4—112no—
325C22×C4—224no—
326C22×C4—224no—
327C22×C4—224no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4—222no—
331C22×C4—442no—
332C22×C4—442no—
333C22×C4—442no—
334C22×C4D4×D1112yes—
335C22×C4C23×D1111yescharacteristic
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—448no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—444no—
350C4⋊C4—444no—
351C22⋊C4—44no—
352C22⋊C4—444no—
353C22⋊C4—442no—
354C22⋊C4—444no—
355C42—22no—
356C42—224no—
357C42—222no—
358C42—444no—
359C42—442no—
360C11#2362711yescharacteristic, complemented, Sylow
361C23—22no—
362C23—42no—
363C23—42no—
364C23—41no—
365C23—41no—
366C23—112no—
367C23—112no—
368C23—112no—
369C23—222no—
370C23—222no—
371C23C2×D4×D1111yescharacteristic
372Q8—224no—
373Q8—442no—
374D4—24no—
375D4—42no—
376D4—448no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—112no—
386C2×C4—112no—
387C2×C4—112no—
388C2×C4—118no—
389C2×C4—118no—
390C2×C4—114no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—448no—
395C2×C4—448no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—441no—
403C2×C4C2×D4×D1111yescharacteristic
404C2×C4#41×D1111yescharacteristic
405C2×C4#41×D1112yes—
406C2×C4#41×D1112yes—
407C8—42no—
408C8—442no—
409C22—44no—
410C22—42no—
411C22—82no—
412C22—81no—
413C22—81no—
414C22—114no—
415C22—224no—
416C22—224no—
417C22—222no—
418C22—222no—
419C22D11×#12111yescharacteristic
420C22D11×#12311yescharacteristic
421C22D11×#12411yescharacteristic
422C22D11×#13512yes—
423C22#1062330412yes—
424C4—42no—
425C4—82no—
426C4—81no—
427C4—114no—
428C4—224no—
429C4—442no—
430C4—882no—
431C4—881no—
432C4D11×#12312yes—
433C4D11×#12612yes—
434C2—82no—
435C2—224no—
436C2D11×#39711yescharacteristic
437C2#1307806812yes—
438C2#1307852812yes—
439C2#1307893711yescharacteristic
440C2#1307896011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2073C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenter#2073D11
hypocenterC11#23627
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2073

Complements

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

NH ≅ G/Ntype
3. #13071022C2semidirect
4. #13070036C2semidirect
5. #13070035C2semidirect
6. #13070029C2semidirect
7. #13070028C2semidirect
8. #13070022C2semidirect
9. #13068331C2semidirect
10. D11×#336C2semidirect
11. C11×#2073C2semidirect
147. #2073D11semidirect
360. C11#23627semidirect

Maximal subgroups

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

subgroupindex
C2×#106223852
#130711032
#130710222
#130700362
#130700352
#130700292
#130700282
#130700222
#130683312
D11×#3362
C11×#20732
#2362711