Finite Group Databasebeta

← #14737719

Subgroups — #14737719

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079130C211yesmaximal, characteristic, complemented
2#13078779C212yesmaximal
3C8×#4339C211yesmaximal, characteristic
4#13068021C211yesmaximal, characteristic, complemented
5#13068016C211yesmaximal, characteristic, complemented
6#13068011C211yesmaximal, characteristic, complemented
7#13068006C211yesmaximal, characteristic, complemented
8#13067999C212yesmaximal, complemented
9#13067992C212yesmaximal, complemented
10#13067327C212yesmaximal, complemented
11C11×#1568C211yesmaximal, characteristic, complemented
12C4×#4339C2211yescharacteristic
13#10623001C2212yes—
14C11×#432C2212yes—
15C2×C4×C8×C11C2211yescharacteristic
16C8×C22⋊D11—21no—
17C8×C22⋊D11—21no—
18#10622719—21no—
19#10622719—21no—
20#10622538C2211yescharacteristic
21#10622463C2212yes—
22#10622462C2212yes—
23#10622455C2212yes—
24#10622454C2212yes—
25#10622346—22no—
26#10622336—22no—
27#10622329—22no—
28#10622323—22no—
29C8×D44C2211yescharacteristic
30C8×D44C2211yescharacteristic
31#10622298—21no—
32C4×C8×D11—21no—
33#10622296—21no—
34#10622296—21no—
35#10622295C2211yescharacteristic
36#10622295C2211yescharacteristic
37#10622293C2212yes—
38C8×Dic22C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×#335C2211yescharacteristic
41C11×#335C2211yescharacteristic
42C11×#334C2212yes—
43#10622120C2212yes—
44#10622120C2212yes—
45#10622119C2212yes—
46#10622119C2212yes—
47C2×#4339D411yescharacteristic
48C22×C8×C11D411yescharacteristic
49C22×C8×C11D411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C4×C22⋊D11—21no—
52C4×C22⋊D11—21no—
53#66979—22no—
54#66979D411yescharacteristic
55#66977—22no—
56#66977—22no—
57C2×Dic44—22no—
58C2×#4314—22no—
59C2×C8×D11—21no—
60C2×C8×D11—21no—
61C4×D44D411yescharacteristic
62C4×D44C2311yescharacteristic
63#66925—21no—
64C42×D11—21no—
65#66923—22no—
66#66922C2312yes—
67#66922C2312yes—
68C4×Dic22—22no—
69C4×Dic22—22no—
70C4×Dic22D411yescharacteristic
71C4×Dic22C2311yescharacteristic
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C22⋊C8—22no—
75C11×#97—22no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80C22⋊(C11⋊C8)—21no—
81#66885—22no—
82(C2×D11)⋊C8—21no—
83(C2×D11)⋊C8—21no—
84#66882—21no—
85#66882—21no—
86#66882—21no—
87#66882—21no—
88#66882—22no—
89#66881—22no—
90#66881—22no—
91#66881—22no—
92#66880—22no—
93#66880—22no—
94#66880—22no—
95Dic11⋊C8—21no—
96Dic11⋊C8—21no—
97C8×Dic11—21no—
98C8×Dic11—21no—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4×C11⋊C8—21no—
102#19273—111nomaximal, Sylow
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C2×C22⋊D11—21no—
107#4339—22no—
108#4339—22no—
109C2×D44C2×D411yescharacteristic
110C2×C4×D11—21no—
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22C2×D411yescharacteristic
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128C22⋊Dic11—21no—
129C22⋊Dic11—42no—
130(C2×D11)⋊C4—21no—
131(C2×D11)⋊C4—21no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11C2×D411yescharacteristic
137C4⋊Dic11C2×D411yescharacteristic
138Dic11⋊C4—21no—
139Dic11⋊C4—21no—
140Dic11⋊C4—42no—
141Dic11⋊C4—42no—
142C4×Dic11—21no—
143C4×Dic11—21no—
144C4×Dic11—21no—
145C4×Dic11—42no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148Dic44—44no—
149#4314—44no—
150C8×D11—42no—
151C8×D11—42no—
152#3160—111no—
153#3116—112no—
154C8×#41—111no—
155#1676—111no—
156#1675—111no—
157#1674—111no—
158#1673—111no—
159#1672—112no—
160#1671—112no—
161#1568D1111yescharacteristic, complemented
162#1554—112no—
163C23×C11#12111yescharacteristic
164C22×D11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—41no—
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C22⋊D11—24no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182D44—21no—
183D44#13512yes—
184C4×D11—24no—
185C4×D11—42no—
186C4×D11—41no—
187C4×D11—41no—
188Dic22—21no—
189Dic22—42no—
190Dic22—42no—
191Dic22—82no—
192Dic22#13512yes—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11—42no—
196C8×C11—42no—
197C8×C11#13712yes—
198C8×C11#13712yes—
199C11⋊C8—41no—
200C11⋊C8—41no—
201#533—112no—
202C4×#41—111no—
203#500—111no—
204#500—111no—
205#499—221no—
206#499—221no—
207#498—112no—
208#485—222no—
209#477—112no—
210#476—112no—
211#462—112no—
212#461—112no—
213#452—222no—
214C8×Q8—111no—
215C8×Q8—111no—
216#441—222no—
217#440—222no—
218C8×D4—111no—
219C8×D4—111no—
220C8×D4—221no—
221C8×D4—221no—
222#432C2×D1112yes—
223#431—111no—
224#431—221no—
225#427—221no—
226#427—221no—
227C2×C4×C8—221no—
228C2×C4×C8C2×D1111yescharacteristic
229#335C2×D1111yescharacteristic
230#335C2×D1111yescharacteristic
231#334C2×D1112yes—
232#333—112no—
233#333—112no—
234#332—112no—
235#332—112no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11C2×#12111yescharacteristic
240C2×D11—22no—
241C2×D11—41no—
242C2×D11—41no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11C2×#13511yescharacteristic
248C4×C11C2×#13511yescharacteristic
249C4×C11C2×#13711yescharacteristic
250C4×C11C2×#13711yescharacteristic
251Dic11—22no—
252Dic11—41no—
253Dic11—41no—
254Dic11—82no—
255Dic11—82no—
256C2×#41—111no—
257C2×Q16—222no—
258C2×SD16—222no—
259C22×C8—221no—
260C22×C8—221no—
261C22×C8D4411yescharacteristic
262C22×C8D4411yescharacteristic
263C4⋊Q8—112no—
264C4⋊Q8—112no—
265#125—222no—
266C22⋊Q8—222no—
267C22⋊Q8—222no—
268C4×Q8—111no—
269C4×Q8—111no—
270C4×Q8—222no—
271C4×Q8—222no—
272C4×D4—111no—
273C4×D4—111no—
274C4×D4—221no—
275C4×D4—221no—
276#117—111no—
277#117—221no—
278#117—222no—
279C2×C42—221no—
280C2×C42C22×D1111yescharacteristic
281#107—222no—
282#107—221no—
283#107—221no—
284#107—221no—
285#107—221no—
286#106—222no—
287#106—222no—
288#106—222no—
289C4⋊C8—111no—
290C4⋊C8—111no—
291C4⋊C8—221no—
292C4⋊C8—221no—
293C4⋊C8C22×D1112yes—
294C4⋊C8C22×D1112yes—
295#103—222no—
296#103—222no—
297#103—222no—
298#102—222no—
299C22⋊C8—22no—
300C22⋊C8—221no—
301C22⋊C8—221no—
302C22⋊C8—221no—
303#97—22no—
304C4×C8—221no—
305C4×C8—221no—
306C4×C8—221no—
307C4×C8D4411yescharacteristic
308C4×C8D4411yescharacteristic
309C4×C8C22×D1111yescharacteristic
310C4×C8C22×D1111yescharacteristic
311C2×C11—41no—
312C2×C11#303911yescharacteristic
313C2×C11#305011yescharacteristic
314C2×C11#306711yescharacteristic
315D11—42no—
316#41—222no—
317#41—222no—
318C2×Q8—111no—
319C2×Q8—222no—
320C2×Q8—222no—
321C2×D4—111no—
322C2×D4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4C2×D4411yescharacteristic
327C22×C4D4×D1111yescharacteristic
328C22×C4#434311yescharacteristic
329Q16—444no—
330SD16—444no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—442no—
338C2×C8—442no—
339C2×C8C2×D4411yescharacteristic
340C2×C8C2×D4411yescharacteristic
341C2×C8C2×D4411yescharacteristic
342C2×C8C2×D4411yescharacteristic
343C4⋊C4—111no—
344C4⋊C4—111no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—222no—
350C4⋊C4—222no—
351C4⋊C4—442no—
352C4⋊C4—442no—
353C22⋊C4—221no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C22⋊C4—442no—
357C42—221no—
358C42—221no—
359C42—221no—
360C42—442no—
361C42C2×D4411yescharacteristic
362C42D4×D1111yescharacteristic
363C42#434311yescharacteristic
364C42C23×D1111yescharacteristic
365C11#1927311yescharacteristic, complemented, Sylow
366C23—221no—
367C23#6694811yescharacteristic
368Q8—112no—
369Q8—221no—
370Q8—442no—
371Q8—442no—
372Q8—882no—
373D4—112no—
374D4—224no—
375D4—221no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—224no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—442no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4#6694811yescharacteristic
391C2×C4#6694811yescharacteristic
392C2×C4#6694811yescharacteristic
393C2×C4C22×D4411yescharacteristic
394C2×C4C2×D4×D1111yescharacteristic
395C2×C4C2×#434311yescharacteristic
396C8—21no—
397C8—21no—
398C8—42no—
399C8—42no—
400C8—441no—
401C8—441no—
402C8#6696212yes—
403C8#6696212yes—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—222no—
408C22—441no—
409C22—441no—
410C22C2×#6694811yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—222no—
416C4—441no—
417C4—441no—
418C4—882no—
419C4—882no—
420C4C2×#6696211yescharacteristic
421C4C2×#6696211yescharacteristic
422C4D11×#13511yescharacteristic
423C4D11×#13511yescharacteristic
424C2—41no—
425C2—442no—
426C2#1307810411yescharacteristic
427C2#1307819811yescharacteristic
428C2#1307833711yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1568C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#1568D11
hypocenterC11#19273
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
1. #13079130C2semidirect
4. #13068021C2semidirect
5. #13068016C2semidirect
6. #13068011C2semidirect
7. #13068006C2semidirect
8. #13067999C2semidirect
9. #13067992C2semidirect
10. #13067327C2semidirect
11. C11×#1568C2semidirect
161. #1568D11semidirect
365. C11#19273semidirect

Maximal subgroups

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

subgroupindex
#130791302
#130787792
C8×#43392
#130680212
#130680162
#130680112
#130680062
#130679992
#130679922
#130673272
C11×#15682
#1927311