Finite Group Databasebeta

← #14737306

Subgroups — #14737306

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079737C211yesmaximal, characteristic
3#13077362C211yesmaximal, characteristic
4#13068188C212yesmaximal, complemented
5#13068160C212yesmaximal, complemented
6#13068064C212yesmaximal, complemented
7#13068036C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067273C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3139C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66960—21no—
15#10623008C2211yescharacteristic
16C11×#491—22no—
17C11×#487C2212yes—
18C11×#487C2212yes—
19C11×#419—21no—
20C11×#419—21no—
21C4×C11×M16C2211yescharacteristic
22#10622742—21no—
23#10622701—21no—
24#10622700C2212yes—
25#10622700C2212yes—
26#10622697C2212yes—
27#10622696C2212yes—
28#10622691—21no—
29#10622661—22no—
30#10622640—21no—
31#10622633—21no—
32#10622580—22no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622319—22no—
37#10622301C2212yes—
38C8×D44C2212yes—
39#10622185C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2211yescharacteristic
42#10622185C2212yes—
43#10622184C2211yescharacteristic
44#10622184C2211yescharacteristic
45#10622096C2212yes—
46#10622095C2212yes—
47C22×Q8×C11—21no—
48C2×#4339—21no—
49C2×C11×M16D411yescharacteristic
50C2×C11×M16D411yescharacteristic
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8C2312yes—
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C11×#117—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C2×#4325—22no—
67#66983—21no—
68#66983D412yes—
69C22×C11⋊C8—21no—
70C22×C11⋊C8—21no—
71#66960—44no—
72C2×#4313—22no—
73C2×C8×D11—22no—
74#66928—21no—
75#66927D411yescharacteristic
76C4×D44—21no—
77C4×D44C2312yes—
78#66922D411yescharacteristic
79C11×#103—22no—
80C11×#103—22no—
81C11×#103—22no—
82C11×#103—22no—
83C11×#97D412yes—
84C4×C8×C11C2312yes—
85#66899—22no—
86C22⋊(C11⋊C8)—21no—
87(C2×D11)⋊C8—22no—
88(C2×D11)⋊C8—22no—
89#66873—22no—
90#66873—22no—
91#66873—22no—
92#66872—22no—
93#66871—22no—
94#66871—22no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4×C11⋊C8—21no—
103#19235—111nomaximal, Sylow
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—41no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C22×C4×C11—41no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×C22⋊D11—22no—
115#4339—42no—
116#4339—42no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44C2×D412yes—
120C2×C4×D11—22no—
121C2×Dic22—21no—
122C11×M16—22no—
123C11×M16—22no—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D412yes—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11—41no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11#4111yescharacteristic
141C42×C11C2411yescharacteristic
142#4325—82no—
143(C2×D11)⋊C4—22no—
144(C2×D11)⋊C4—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11C2×D412yes—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—42no—
153C2×C11⋊C8—81no—
154#4313—44no—
155C8×D11—44no—
156#3246—111no—
157#3226—111no—
158#3139D1111yescharacteristic, complemented
159#2935—111no—
160#1703—112no—
161#1699—112no—
162#1683—112no—
163#1679—112no—
164#1565—111no—
165#1542—111no—
166C2×#332—111no—
167C23×C11#12111yescharacteristic
168C22×D11—22no—
169Q8×C11—42no—
170Q8×C11—42no—
171Q8×C11—41no—
172Q8×C11—41no—
173Q8×C11—81no—
174Q8×C11—82no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—82no—
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#13512yes—
186C2×C4×C11AGL(1,ℤ/8)12yes—
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C22⋊D11—44no—
191C2×Dic11—22no—
192D44—22no—
193D44—22no—
194D44—42no—
195D44—81no—
196C4×D11—42no—
197C4×D11—42no—
198Dic22—42no—
199C8×C11—22no—
200C8×C11—22no—
201C11⋊C8—41no—
202C11⋊C8—41no—
203C11⋊C8—41no—
204C11⋊C8—42no—
205C11⋊C8—41no—
206C2×#131—221no—
207#533C2×D1111yescharacteristic
208#532—111no—
209C2×C4⋊Q8C2×D1111yescharacteristic
210#500—221no—
211#491—22no—
212#487C2×D1112yes—
213#487C2×D1112yes—
214#486—221no—
215#480—222no—
216#476—112no—
217#475—221no—
218#474—112no—
219#474—112no—
220#465—222no—
221#461—112no—
222#460—221no—
223#436—112no—
224#435—222no—
225C8×D4—112no—
226#431—111no—
227C2×C4⋊C8—111no—
228C2×C4⋊C8—111no—
229#419—21no—
230#419—21no—
231#408—221no—
232C4×M16C2×D1111yescharacteristic
233#335—112no—
234#334—112no—
235#333—111no—
236#333—111no—
237#332—112no—
238#332—112no—
239#332—111no—
240#332—111no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11#46312yes—
244C22×C11C2×#12111yescharacteristic
245C2×D11—42no—
246C2×D11—42no—
247C2×D11—42no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—82no—
252C4×C11—81no—
253C4×C11—81no—
254C4×C11#46312yes—
255C4×C11C2×#13511yescharacteristic
256C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
257C4×C11#57711yescharacteristic
258C4×C11#57811yescharacteristic
259Dic11—42no—
260C2×#41—221no—
261C22×Q8—21no—
262C2×SD16—222no—
263#131—444no—
264C2×M16—222no—
265C2×M16C22⋊D1111yescharacteristic
266C2×M16C22⋊D1111yescharacteristic
267C22×C8—221no—
268C22×C8—221no—
269C22×C8—222no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8—111no—
274C4⋊Q8C22×D1112yes—
275C4⋊Q8C22×D1111yescharacteristic
276C4⋊Q8C22×D1111yescharacteristic
277#127—111no—
278#125—21no—
279#124—221no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282#121—112no—
283#121—221no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—112no—
287C4×D4—221no—
288#117—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C42C22×D1111yescharacteristic
292#107—222no—
293#107—222no—
294#106—222no—
295C4⋊C8—111no—
296C4⋊C8—111no—
297C4⋊C8—112no—
298C4⋊C8—111no—
299C4⋊C8—111no—
300C4⋊C8—221no—
301C4⋊C8—221no—
302#103—22no—
303#103—22no—
304#103—22no—
305#103—22no—
306#103—222no—
307#102—222no—
308#102—222no—
309#102—222no—
310C22⋊C8—221no—
311C22⋊C8—222no—
312C22⋊C8—222no—
313#97C22⋊D1112yes—
314C4×C8—221no—
315C4×C8C22×D1112yes—
316C2×C11—22no—
317C2×C11C2×#46311yescharacteristic
318C2×C11#306311yescharacteristic
319C2×C11#306911yescharacteristic
320D11—82no—
321#41—442no—
322#41—442no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—41no—
327C2×Q8—42no—
328C2×Q8—42no—
329C2×Q8—221no—
330C2×D4—112no—
331C2×D4—222no—
332C2×D4—221no—
333C2×D4—221no—
334C22×C4—41no—
335C22×C4—222no—
336C22×C4D4×D1111yescharacteristic
337C22×C4#434111yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339SD16—882no—
340M16—22no—
341M16—22no—
342M16—444no—
343C2×C8—221no—
344C2×C8—221no—
345C2×C8—222no—
346C2×C8—221no—
347C2×C8—221no—
348C2×C8—444no—
349C2×C8—442no—
350C2×C8—881no—
351C2×C8C2×C22⋊D1112yes—
352C2×C8C2×C22⋊D1112yes—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—112no—
364C4⋊C4—221no—
365C22⋊C4—41no—
366C22⋊C4—222no—
367C22⋊C4—222no—
368C42—41no—
369C42D4×D1111yescharacteristic
370C42#434111yescharacteristic
371C42C2×C22⋊D1111yescharacteristic
372C42C23×D1111yescharacteristic
373C11#1923511yescharacteristic, complemented, Sylow
374C23—222no—
375C23#6699111yescharacteristic
376Q8—41no—
377Q8—41no—
378Q8—42no—
379Q8—42no—
380Q8—81no—
381Q8—82no—
382Q8—442no—
383D4—222no—
384D4—222no—
385D4—444no—
386D4—442no—
387D4—881no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—82no—
395C2×C4—222no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4#6699111yescharacteristic
399C2×C4#6699111yescharacteristic
400C2×C4#6699111yescharacteristic
401C2×C4#6700212yes—
402C2×C4#6700312yes—
403C2×C4C2×D4×D1111yescharacteristic
404C2×C4C2×#434111yescharacteristic
405C2×C4C22×C22⋊D1111yescharacteristic
406C8—22no—
407C8—22no—
408C8—442no—
409C8—441no—
410C8—441no—
411C8—441no—
412C8—441no—
413C22—21no—
414C22—21no—
415C22—442no—
416C22—442no—
417C22—442no—
418C22#1062267012yes—
419C22C2×#6699111yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—82no—
424C4—81no—
425C4—81no—
426C4—442no—
427C4#1062267012yes—
428C4#1062330911yescharacteristic
429C4#1062331011yescharacteristic
430C4C2×#6700211yescharacteristic
431C4C2×#6700311yescharacteristic
432C2—22no—
433C2—882no—
434C2C2×#1062267011yescharacteristic
435C2#1307830111yescharacteristic
436C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3139C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3139D11
hypocenterC11#19235
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
4. #13068188C2semidirect
5. #13068160C2semidirect
6. #13068064C2semidirect
7. #13068036C2semidirect
8. #13067368C2semidirect
9. #13067273C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3139C2semidirect
158. #3139D11semidirect
373. C11#19235semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130797372
#130773622
#130681882
#130681602
#130680642
#130680362
#130673682
#130672732
C2×#106221852
C11×#31392
#1923511