Finite Group Databasebeta

← #14737273

Subgroups — #14737273

Order 2816.

652 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
1#13079928C211yesmaximal, characteristic
2#13079541C211yesmaximal, characteristic
3#13077362C211yesmaximal, characteristic
4#13068126C212yesmaximal, complemented
5#13068112C212yesmaximal, complemented
6#13068002C212yesmaximal, complemented
7#13067988C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067273C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, 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#10622840—22no—
23#10622742—21no—
24#10622698—21no—
25#10622697C2212yes—
26#10622696C2212yes—
27#10622696C2212yes—
28#10622696C2212yes—
29#10622694—21no—
30#10622661—22no—
31#10622640—21no—
32#10622633—21no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622319—22no—
37#10622301C2212yes—
38C8×D44C2212yes—
39#10622185C2211yescharacteristic
40#10622185C2211yescharacteristic
41#10622185C2212yes—
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⋊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—
67C2×#4325—22no—
68C2×#4325—22no—
69#66983—21no—
70#66983D412yes—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73#66960—44no—
74C2×#4313—22no—
75C2×C8×D11—22no—
76#66928—21no—
77#66927D411yescharacteristic
78C4×D44—21no—
79C4×D44C2312yes—
80#66922D411yescharacteristic
81C11×#107—22no—
82C11×#107—22no—
83C11×#106—22no—
84C11×#106—22no—
85C11×#97D412yes—
86C4×C8×C11C2312yes—
87#66899—22no—
88#66899—22no—
89#66899—22no—
90C22⋊(C11⋊C8)—21no—
91(C2×D11)⋊C8—22no—
92(C2×D11)⋊C8—22no—
93#66873—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#19232—111nomaximal, Sylow
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—41no—
108C2×Q8×C11—81no—
109C2×Q8×C11—81no—
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×M16SD1614yescomplemented
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D412yes—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
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#4325—82no—
144#4325—82no—
145(C2×D11)⋊C4—22no—
146(C2×D11)⋊C4—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11C2×D412yes—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—42no—
155C2×C11⋊C8—81no—
156#4313—44no—
157C8×D11—44no—
158#3246—111no—
159#3206—111no—
160#3165D1111yescharacteristic, complemented
161#2935—111no—
162#1693—112no—
163#1691—112no—
164#1673—112no—
165#1671—112no—
166#1565—111no—
167#1542—111no—
168C2×#332—111no—
169C23×C11#12111yescharacteristic
170C22×D11—22no—
171Q8×C11—41no—
172Q8×C11—42no—
173Q8×C11—42no—
174Q8×C11—41no—
175Q8×C11—81no—
176Q8×C11—82no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—82no—
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11C2×SD1612yes—
188C2×C4×C11#13712yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C22⋊D11—44no—
193C2×Dic11—22no—
194D44—22no—
195D44—22no—
196D44—42no—
197D44—81no—
198C4×D11—42no—
199C4×D11—42no—
200Dic22—42no—
201C8×C11—22no—
202C8×C11C2×SD1614yes—
203C11⋊C8—41no—
204C11⋊C8—41no—
205C11⋊C8—42no—
206C11⋊C8—41no—
207C11⋊C8—41no—
208C2×#131—221no—
209#533C2×D1111yescharacteristic
210#532—111no—
211C2×C4⋊Q8C2×D1111yescharacteristic
212#501—22no—
213#500C2×D1112yes—
214#498C2×D1112yes—
215#492—221no—
216#487—221no—
217#476—112no—
218#475—221no—
219#465—222no—
220#461—112no—
221#461—112no—
222#461—112no—
223#460—221no—
224#448—222no—
225#436—112no—
226#435—222no—
227C8×D4—112no—
228#431—111no—
229#428—21no—
230#428—21no—
231C2×C4⋊C8—111no—
232C2×C4⋊C8—111no—
233#408—221no—
234C4×M16C2×D1111yescharacteristic
235#335—112no—
236#334—112no—
237#333—111no—
238#333—111no—
239#332—112no—
240#332—112no—
241#332—111no—
242#332—111no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11#46112yes—
246C22×C11C2×#12111yescharacteristic
247C2×D11—42no—
248C2×D11—42no—
249C2×D11—42no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—82no—
254C4×C11—81no—
255C4×C11—81no—
256C4×C11#46112yes—
257C4×C11C22×SD1611yescharacteristic
258C4×C11C2×#13711yescharacteristic
259C4×C11#57611yescharacteristic
260C4×C11#57711yescharacteristic
261Dic11—42no—
262C2×#41—221no—
263C22×Q8—21no—
264C2×SD16—222no—
265C2×SD16—222no—
266C2×SD16—222no—
267#131—444no—
268C2×M16—222no—
269C2×M16C22⋊D1111yescharacteristic
270C2×M16C22⋊D1111yescharacteristic
271C22×C8—221no—
272C22×C8—221no—
273C22×C8—222no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—111no—
278C4⋊Q8C22×D1112yes—
279C4⋊Q8C22×D1111yescharacteristic
280C4⋊Q8C22×D1111yescharacteristic
281#127—111no—
282#125—21no—
283#124—221no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286#121—112no—
287#121—221no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×D4—112no—
291C4×D4—221no—
292#117—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C42C22×D1111yescharacteristic
296#107—22no—
297#107—22no—
298#106—22no—
299#106—22no—
300#106—222no—
301C4⋊C8—111no—
302C4⋊C8—111no—
303C4⋊C8—112no—
304C4⋊C8—111no—
305C4⋊C8—111no—
306C4⋊C8—221no—
307C4⋊C8—221no—
308#103—222no—
309#103—222no—
310#103—222no—
311#102—222no—
312C22⋊C8—221no—
313C22⋊C8—222no—
314C22⋊C8—222no—
315#97C22⋊D1112yes—
316C4×C8—221no—
317C4×C8C22×D1112yes—
318C2×C11—22no—
319C2×C11C2×#46111yescharacteristic
320C2×C11#306211yescharacteristic
321C2×C11#306911yescharacteristic
322D11—82no—
323#41—442no—
324#41—442no—
325C2×Q8—21no—
326C2×Q8—22no—
327C2×Q8—21no—
328C2×Q8—41no—
329C2×Q8—81no—
330C2×Q8—81no—
331C2×Q8—221no—
332C2×D4—112no—
333C2×D4—222no—
334C2×D4—221no—
335C2×D4—221no—
336C22×C4—41no—
337C22×C4—222no—
338C22×C4D4×D1111yescharacteristic
339C22×C4#434111yescharacteristic
340C22×C4C2×C22⋊D1111yescharacteristic
341SD16—882no—
342SD16—882no—
343SD16—882no—
344M16—22no—
345M16—444no—
346M16#432514yescomplemented
347C2×C8—221no—
348C2×C8—221no—
349C2×C8—222no—
350C2×C8—221no—
351C2×C8—221no—
352C2×C8—442no—
353C2×C8—444no—
354C2×C8—881no—
355C2×C8C2×C22⋊D1112yes—
356C2×C8C2×C22⋊D1112yes—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—112no—
368C4⋊C4—221no—
369C22⋊C4—41no—
370C22⋊C4—222no—
371C22⋊C4—222no—
372C42—41no—
373C42D4×D1111yescharacteristic
374C42#434111yescharacteristic
375C42C2×C22⋊D1111yescharacteristic
376C42C23×D1111yescharacteristic
377C11#1923211yescharacteristic, complemented, Sylow
378C23—222no—
379C23#6699111yescharacteristic
380Q8—41no—
381Q8—42no—
382Q8—42no—
383Q8—41no—
384Q8—81no—
385Q8—82no—
386Q8—442no—
387D4—222no—
388D4—222no—
389D4—444no—
390D4—442no—
391D4—881no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—82no—
399C2×C4—222no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4#6699111yescharacteristic
403C2×C4#6699111yescharacteristic
404C2×C4#6699111yescharacteristic
405C2×C4C2×#432512yes—
406C2×C4#6699512yes—
407C2×C4C2×D4×D1111yescharacteristic
408C2×C4C2×#434111yescharacteristic
409C2×C4C22×C22⋊D1111yescharacteristic
410C8—22no—
411C8—442no—
412C8—441no—
413C8—441no—
414C8—441no—
415C8—441no—
416C8C2×#432514yes—
417C22—21no—
418C22—21no—
419C22—442no—
420C22—442no—
421C22—442no—
422C22#1062269612yes—
423C22C2×#6699111yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—82no—
428C4—81no—
429C4—81no—
430C4—442no—
431C4#1062269612yes—
432C4#1062330511yescharacteristic
433C4#1062330611yescharacteristic
434C4C22×#432511yescharacteristic
435C4C2×#6699511yescharacteristic
436C2—22no—
437C2—882no—
438C2C2×#1062269611yescharacteristic
439C2#1307829011yescharacteristic
440C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3165C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3165D11
hypocenterC11#19232
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. #13068126C2semidirect
5. #13068112C2semidirect
6. #13068002C2semidirect
7. #13067988C2semidirect
8. #13067368C2semidirect
9. #13067273C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3165C2semidirect
123. C11×M16SD16semidirect
160. #3165D11semidirect
346. M16#4325semidirect
377. C11#19232semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130795412
#130773622
#130681262
#130681122
#130680022
#130679882
#130673682
#130672732
C2×#106221852
C11×#31652
#1923211