Finite Group Databasebeta

← #14737352

Subgroups — #14737352

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13068108C212yesmaximal, complemented
5#13068090C212yesmaximal, complemented
6#13067984C212yesmaximal, complemented
7#13067966C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067263C211yesmaximal, characteristic
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3229C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66995—21no—
15C2×#66995—21no—
16#10623008C2211yescharacteristic
17C11×#498—21no—
18C11×#487—21no—
19C11×#483—22no—
20C11×#475C2212yes—
21C11×#475C2212yes—
22C11×#431C2211yescharacteristic
23#10622705C2212yes—
24#10622699—22no—
25#10622698C2212yes—
26#10622697—21no—
27#10622696—21no—
28#10622661—22no—
29#10622640C2212yes—
30#10622637—22no—
31#10622637C2212yes—
32Q8×C11⋊C8C2212yes—
33#10622633C2212yes—
34#10622612—21no—
35#10622610—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622185C2212yes—
40#10622185C2212yes—
41#10622124C2211yescharacteristic
42#10622124C2211yescharacteristic
43#10622123C2211yescharacteristic
44#10622123C2211yescharacteristic
45#10622118C2212yes—
46#10622117C2212yes—
47C22×Q8×C11—21no—
48C2×#4339—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2312yes—
55C11×#125—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8D412yes—
58C4×Q8×C11—21no—
59C4×Q8×C11C2312yes—
60C11×#117—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4326—22no—
65C2×#4326—22no—
66#66995—44no—
67#66995—44no—
68C2×#4325—22no—
69C2×#4325—22no—
70C2×#4325—22no—
71#66983—21no—
72#66983—21no—
73C2×#4318D411yescharacteristic
74C2×#4318D411yescharacteristic
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77#66928—21no—
78#66927C2311yescharacteristic
79C4×D44—21no—
80C4×D44—21no—
81#66922C2311yescharacteristic
82C11×#106—22no—
83C11×#106—22no—
84C11×C4⋊C8C2311yescharacteristic
85C11×C4⋊C8C2311yescharacteristic
86C11×#103—22no—
87C11×#103—22no—
88C11×C22⋊C8—21no—
89C4×C8×C11—21no—
90#66899—22no—
91#66873—22no—
92#66872—22no—
93C4⋊(C11⋊C8)—21no—
94C4⋊(C11⋊C8)—21no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867—22no—
101#66867D412yes—
102C4×C11⋊C8—22no—
103C4×C11⋊C8C2312yes—
104#19239—111nomaximal, Sylow
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—41no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×Q8×C11C2×D412yes—
111C22×C4×C11—41no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C2×C22⋊D11—41no—
116#4339—42no—
117#4339—42no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×C4×D11—41no—
122C2×Dic22—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4C2×D412yes—
135C11×C22⋊C4—22no—
136C42×C11—22no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141#4326—44no—
142#4326—44no—
143#4325—44no—
144#4325—44no—
145#4325—82no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150#4318—22no—
151#4318SD1614yescomplemented
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—42no—
156C2×C11⋊C8—81no—
157C2×C11⋊C8C2×D412yes—
158C2×C11⋊C8C2×D412yes—
159#3246—111no—
160#3229D1111yescharacteristic, complemented
161#3152—111no—
162#2962—111no—
163#1690—112no—
164#1686—112no—
165#1670—112no—
166#1666—112no—
167#1565—111no—
168#1540—111no—
169C2×#332—111no—
170C23×C11#12111yescharacteristic
171C22×D11—41no—
172Q8×C11—22no—
173Q8×C11—22no—
174Q8×C11—42no—
175Q8×C11—42no—
176Q8×C11—81no—
177Q8×C11—82no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—82no—
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11C2×SD1612yes—
189C2×C4×C11AGL(1,ℤ/8)12yes—
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C22⋊D11—82no—
194C2×Dic11—41no—
195D44—41no—
196D44—41no—
197D44—41no—
198D44—41no—
199D44—81no—
200C4×D11—82no—
201Dic22—41no—
202Dic22—41no—
203C8×C11—41no—
204C8×C11—41no—
205C11⋊C8—22no—
206C11⋊C8—41no—
207C11⋊C8—41no—
208C11⋊C8—42no—
209C11⋊C8C2×SD1614yes—
210C2×#137—221no—
211C2×#137—221no—
212#533C2×D1111yescharacteristic
213#532—111no—
214C2×C4⋊Q8C2×D1111yescharacteristic
215#498—21no—
216#497—222no—
217#494—112no—
218#492—112no—
219#487—21no—
220#483—22no—
221#476—221no—
222#475—112no—
223#475C2×D1112yes—
224#475C2×D1112yes—
225#465—222no—
226#461—221no—
227#460—112no—
228#446—112no—
229#446—222no—
230C8×Q8—112no—
231#431C2×D1111yescharacteristic
232#424—221no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8—111no—
235#405—221no—
236C4×M16—111no—
237#335—112no—
238#334—112no—
239#332—112no—
240#332—112no—
241#332—111no—
242#332—111no—
243#331—111no—
244#331—111no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11#46012yes—
248C22×C11C2×#12111yescharacteristic
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—81no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—82no—
258C4×C11#46012yes—
259C4×C11C22×SD1611yescharacteristic
260C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C4×C11#57711yescharacteristic
262C4×C11#57811yescharacteristic
263Dic11—81no—
264C2×#41—221no—
265C22×Q8—21no—
266#137—444no—
267#137—444no—
268C2×Q16—222no—
269C2×Q16—222no—
270C2×SD16—222no—
271C2×SD16—222no—
272C2×SD16—222no—
273C2×M16—111no—
274C2×M16—111no—
275C22×C8—221no—
276C22×C8—221no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—111no—
281C4⋊Q8C22⋊D1111yescharacteristic
282C4⋊Q8C22⋊D1111yescharacteristic
283C4⋊Q8C22×D1112yes—
284#127—111no—
285#125—21no—
286#124—221no—
287C22⋊Q8—21no—
288C22⋊Q8C22⋊D1112yes—
289#121—221no—
290#121—221no—
291C4×Q8—21no—
292C4×Q8C22×D1112yes—
293C4×D4—221no—
294C4×D4—221no—
295#117—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C42C22×D1111yescharacteristic
299#106—22no—
300#106—22no—
301#106—222no—
302C4⋊C8—111no—
303C4⋊C8—111no—
304C4⋊C8—112no—
305C4⋊C8—222no—
306C4⋊C8—222no—
307C4⋊C8—221no—
308C4⋊C8—221no—
309C4⋊C8C22×D1111yescharacteristic
310C4⋊C8C22×D1111yescharacteristic
311#103—22no—
312#103—22no—
313#103—222no—
314#102—222no—
315C22⋊C8—21no—
316#97—112no—
317#97—222no—
318C4×C8—21no—
319C4×C8—112no—
320C4×C8—222no—
321C2×C11—22no—
322C2×C11C2×#46011yescharacteristic
323C2×C11#306311yescharacteristic
324C2×C11#306911yescharacteristic
325D11—161no—
326#41—442no—
327#41—442no—
328C2×Q8—21no—
329C2×Q8—22no—
330C2×Q8—41no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×Q8—221no—
334C2×Q8C2×C22⋊D1112yes—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—441no—
339C22×C4—41no—
340C22×C4—441no—
341C22×C4D4×D1111yescharacteristic
342C22×C4#434111yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344Q16—444no—
345Q16—444no—
346SD16—444no—
347SD16—444no—
348SD16—882no—
349M16—114no—
350M16—222no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—112no—
354C2×C8—112no—
355C2×C8—221no—
356C2×C8—221no—
357C2×C8—222no—
358C2×C8—442no—
359C2×C8—881no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4C2×C22⋊D1112yes—
372C22⋊C4—22no—
373C22⋊C4—441no—
374C22⋊C4—441no—
375C42—22no—
376C42D4×D1111yescharacteristic
377C42#434111yescharacteristic
378C42C2×C22⋊D1111yescharacteristic
379C42C23×D1111yescharacteristic
380C11#1923911yescharacteristic, complemented, Sylow
381C23—441no—
382C23#6699211yescharacteristic
383Q8—22no—
384Q8—22no—
385Q8—42no—
386Q8—42no—
387Q8—81no—
388Q8—82no—
389Q8—441no—
390Q8—441no—
391D4—441no—
392D4—441no—
393D4—441no—
394D4—441no—
395D4—881no—
396D4—882no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—82no—
404C2×C4—441no—
405C2×C4—882no—
406C2×C4SD16×D1112yes—
407C2×C4#6696712yes—
408C2×C4#6699211yescharacteristic
409C2×C4#6699211yescharacteristic
410C2×C4#6699211yescharacteristic
411C2×C4C2×D4×D1111yescharacteristic
412C2×C4C2×#434111yescharacteristic
413C2×C4C22×C22⋊D1111yescharacteristic
414C8—41no—
415C8—41no—
416C8—114no—
417C8—222no—
418C8—441no—
419C8—441no—
420C8—442no—
421C22—21no—
422C22—21no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22#1062277612yes—
427C22C2×#6699211yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—42no—
433C4—82no—
434C4—881no—
435C4#1062277612yes—
436C4C2×SD16×D1111yescharacteristic
437C4C2×#6696711yescharacteristic
438C4#1062336811yescharacteristic
439C4#1062336911yescharacteristic
440C2—22no—
441C2—1761no—
442C2C2×#1062277611yescharacteristic
443C2#1307830311yescharacteristic
444C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3229C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3229D11
hypocenterC11#19239
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
3. #13077565C2semidirect
4. #13068108C2semidirect
5. #13068090C2semidirect
6. #13067984C2semidirect
7. #13067966C2semidirect
8. #13067369C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3229C2semidirect
151. #4318SD16semidirect
160. #3229D11semidirect
380. C11#19239semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130790732
#130775652
#130681082
#130680902
#130679842
#130679662
#130673692
#130672632
C2×#106221852
C11×#32292
#1923911