Finite Group Databasebeta

← #14737284

Subgroups — #14737284

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079744C211yesmaximal, characteristic
3#13077362C211yesmaximal, characteristic
4#13068136C212yesmaximal, complemented
5#13068112C212yesmaximal, complemented
6#13068012C212yesmaximal, complemented
7#13067988C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067273C211yesmaximal, characteristic, complemented
10C2×#10622184C211yesmaximal, characteristic, complemented
11C11×#3165C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66960—21no—
15#10623008C2211yescharacteristic
16C11×#501—22no—
17C11×#500C2212yes—
18C11×#498C2212yes—
19C11×#428—21no—
20C11×#428—21no—
21C4×C11×M16C2211yescharacteristic
22#10622742—21no—
23#10622701—21no—
24#10622697C2212yes—
25#10622697C2212yes—
26#10622697C2212yes—
27#10622696C2212yes—
28#10622692—21no—
29#10622661—22no—
30#10622640—21no—
31#10622633—21no—
32#10622581—22no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622319—22no—
37#10622301C2212yes—
38C8×D44C2212yes—
39#10622185C2211yescharacteristic
40#10622185C2211yescharacteristic
41#10622184C2212yes—
42#10622184C2212yes—
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⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2312yes—
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×#107—22no—
80C11×#107—22no—
81C11×#106—22no—
82C11×#106—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#66872—22no—
94#66872—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#19233—111nomaximal, Sylow
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—41no—
108C2×Q8×C11—82no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—22no—
114#4339—42no—
115#4339—42no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44C2×D412yes—
119C2×C4×D11—22no—
120C2×Dic22—21no—
121C11×M16—22no—
122C11×M16SD1614yescomplemented
123C2×C8×C11C2×D412yes—
124C2×C8×C11C2×D412yes—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C42×C11—41no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141#4325—82no—
142(C2×D11)⋊C4—22no—
143(C2×D11)⋊C4—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11C2×D412yes—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—42no—
152C2×C11⋊C8—81no—
153#4313—44no—
154C8×D11—44no—
155#3246—111no—
156#3227—111no—
157#3165D1111yescharacteristic, complemented
158#2935—111no—
159#1695—112no—
160#1691—112no—
161#1675—112no—
162#1671—112no—
163#1565—111no—
164#1542—111no—
165C2×#333—111no—
166C23×C11#12111yescharacteristic
167C22×D11—22no—
168Q8×C11—41no—
169Q8×C11—41no—
170Q8×C11—81no—
171Q8×C11—82no—
172Q8×C11—82no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—82no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C2×SD1612yes—
184C2×C4×C11#13712yes—
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C22⋊D11—44no—
189C2×Dic11—22no—
190D44—22no—
191D44—22no—
192D44—42no—
193D44—81no—
194C4×D11—42no—
195C4×D11—42no—
196Dic22—42no—
197C8×C11—22no—
198C8×C11C2×SD1614yes—
199C11⋊C8—41no—
200C11⋊C8—41no—
201C11⋊C8—41no—
202C11⋊C8—42no—
203C11⋊C8—41no—
204C2×#131—221no—
205#533C2×D1111yescharacteristic
206#532—111no—
207C2×C4⋊Q8C2×D1111yescharacteristic
208#501—22no—
209#500C2×D1112yes—
210#498—221no—
211#498C2×D1112yes—
212#486—221no—
213#481—222no—
214#476—112no—
215#476—112no—
216#476—112no—
217#475—221no—
218#465—222no—
219#461—112no—
220#460—221no—
221#436—112no—
222#435—222no—
223C8×D4—112no—
224#431—111no—
225#428—21no—
226#428—21no—
227C2×C4⋊C8—111no—
228C2×C4⋊C8—111no—
229#408—221no—
230C4×M16C2×D1111yescharacteristic
231#335—112no—
232#334—112no—
233#333—112no—
234#333—112no—
235#333—111no—
236#333—111no—
237#332—111no—
238#332—111no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11#46112yes—
242C22×C11C2×#12111yescharacteristic
243C2×D11—42no—
244C2×D11—42no—
245C2×D11—42no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11—82no—
251C4×C11—81no—
252C4×C11#46112yes—
253C4×C11C22×SD1611yescharacteristic
254C4×C11C2×#13711yescharacteristic
255C4×C11#57711yescharacteristic
256C4×C11#57811yescharacteristic
257Dic11—42no—
258C2×#41—221no—
259C22×Q8—21no—
260C2×SD16—222no—
261#131—444no—
262C2×M16—222no—
263C2×M16C22⋊D1111yescharacteristic
264C2×M16C22⋊D1111yescharacteristic
265C22×C8—221no—
266C22×C8—221no—
267C22×C8—222no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—111no—
272C4⋊Q8C22×D1112yes—
273C4⋊Q8C22×D1111yescharacteristic
274C4⋊Q8C22×D1111yescharacteristic
275#127—111no—
276#125—21no—
277#124—221no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280#121—112no—
281#121—221no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×D4—112no—
285C4×D4—221no—
286#117—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C42C22×D1111yescharacteristic
290#107—22no—
291#107—22no—
292#106—22no—
293#106—22no—
294#106—222no—
295#106—222no—
296#106—222no—
297C4⋊C8—111no—
298C4⋊C8—111no—
299C4⋊C8—111no—
300C4⋊C8—111no—
301C4⋊C8—112no—
302C4⋊C8—221no—
303C4⋊C8—221no—
304#103—222no—
305#102—222no—
306#102—222no—
307#102—222no—
308C22⋊C8—221no—
309C22⋊C8—222no—
310C22⋊C8—222no—
311#97C22⋊D1112yes—
312C4×C8—221no—
313C4×C8C22×D1112yes—
314C2×C11—22no—
315C2×C11C2×#46111yescharacteristic
316C2×C11#306311yescharacteristic
317C2×C11#306811yescharacteristic
318D11—82no—
319#41—442no—
320#41—442no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—22no—
324C2×Q8—41no—
325C2×Q8—82no—
326C2×Q8—221no—
327C2×D4—112no—
328C2×D4—222no—
329C2×D4—221no—
330C2×D4—221no—
331C22×C4—41no—
332C22×C4—222no—
333C22×C4D4×D1111yescharacteristic
334C22×C4#434111yescharacteristic
335C22×C4C2×C22⋊D1111yescharacteristic
336SD16—882no—
337M16—22no—
338M16—444no—
339M16#432514yescomplemented
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—222no—
343C2×C8—221no—
344C2×C8—221no—
345C2×C8—442no—
346C2×C8—444no—
347C2×C8—881no—
348C2×C8C2×C22⋊D1112yes—
349C2×C8C2×C22⋊D1112yes—
350C4⋊C4—22no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—21no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—112no—
361C4⋊C4—221no—
362C22⋊C4—41no—
363C22⋊C4—222no—
364C22⋊C4—222no—
365C42—41no—
366C42D4×D1111yescharacteristic
367C42#434111yescharacteristic
368C42C2×C22⋊D1111yescharacteristic
369C42C23×D1111yescharacteristic
370C11#1923311yescharacteristic, complemented, Sylow
371C23—222no—
372C23#6699111yescharacteristic
373Q8—41no—
374Q8—41no—
375Q8—81no—
376Q8—82no—
377Q8—82no—
378Q8—442no—
379D4—222no—
380D4—222no—
381D4—444no—
382D4—442no—
383D4—881no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—82no—
391C2×C4—222no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4#6699111yescharacteristic
395C2×C4#6699111yescharacteristic
396C2×C4#6699111yescharacteristic
397C2×C4C2×#432512yes—
398C2×C4#6699512yes—
399C2×C4C2×D4×D1111yescharacteristic
400C2×C4C2×#434111yescharacteristic
401C2×C4C22×C22⋊D1111yescharacteristic
402C8—22no—
403C8—442no—
404C8—441no—
405C8—441no—
406C8—441no—
407C8—441no—
408C8C2×#432514yes—
409C22—21no—
410C22—21no—
411C22—442no—
412C22—442no—
413C22—442no—
414C22#1062269612yes—
415C22C2×#6699111yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—81no—
420C4—82no—
421C4—81no—
422C4—442no—
423C4#1062269612yes—
424C4#1062330911yescharacteristic
425C4#1062331011yescharacteristic
426C4C22×#432511yescharacteristic
427C4C2×#6699511yescharacteristic
428C2—22no—
429C2—882no—
430C2C2×#1062269611yescharacteristic
431C2#1307830111yescharacteristic
432C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3165C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3165D11
hypocenterC11#19233
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
4. #13068136C2semidirect
5. #13068112C2semidirect
6. #13068012C2semidirect
7. #13067988C2semidirect
8. #13067368C2semidirect
9. #13067273C2semidirect
10. C2×#10622184C2semidirect
11. C11×#3165C2semidirect
122. C11×M16SD16semidirect
157. #3165D11semidirect
339. M16#4325semidirect
370. C11#19233semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130797442
#130773622
#130681362
#130681122
#130680122
#130679882
#130673682
#130672732
C2×#106221842
C11×#31652
#1923311