Finite Group Databasebeta

← #14738588

Subgroups — #14738588

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079839C211yesmaximal, characteristic
2#13079837C211yesmaximal, characteristic
3C2×#10622691C211yesmaximal, characteristic, complemented
4#13077585C211yesmaximal, characteristic
5#13068143C212yesmaximal, complemented
6#13068138C212yesmaximal, complemented
7#13068019C212yesmaximal, complemented
8#13068014C212yesmaximal, complemented
9#13067377C211yesmaximal, characteristic, complemented
10#13067341C211yesmaximal, characteristic, complemented
11C11×#1558C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13#10623010C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C11×#432C2211yescharacteristic
17#10622704C2212yes—
18#10622702—21no—
19#10622697C2212yes—
20#10622693—21no—
21#10622691—21no—
22#10622691—21no—
23#10622691C2212yes—
24#10622691C2212yes—
25#10622584—21no—
26#10622580—21no—
27C2×#66871—21no—
28C2×#66871—21no—
29#10622539C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31#10622463C2212yes—
32#10622455C2212yes—
33#10622451C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622349—21no—
38#10622343—21no—
39(C22⋊D11)⋊C8—21no—
40#10622334—21no—
41#10622327—21no—
42#10622322—21no—
43#10622321—21no—
44#10622315—21no—
45C11×#333C2212yes—
46C11×#333C2212yes—
47#10622119C2212yes—
48#10622119C2212yes—
49#10622118C2212yes—
50#10622117C2212yes—
51C22×Q8×C11—21no—
52C22×Dic22—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2312yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60#66983D411yescharacteristic
61#66982—21no—
62C4×C22⋊D11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65#66977D411yescharacteristic
66C22×C11⋊C8D411yescharacteristic
67C22×C11⋊C8D411yescharacteristic
68C2×#4313—21no—
69C2×C8×D11—21no—
70#66929—21no—
71#66928D411yescharacteristic
72C4×D44C2311yescharacteristic
73#66925—21no—
74#66923D411yescharacteristic
75#66922—21no—
76#66922—21no—
77#66922—21no—
78#66922C2312yes—
79C4×Dic22C2311yescharacteristic
80C11×C4⋊C8C2312yes—
81C11×C4⋊C8C2311yescharacteristic
82C11×C4⋊C8C2311yescharacteristic
83C11×C22⋊C8—21no—
84C11×C22⋊C8—21no—
85C11×#97—21no—
86C11×#97—21no—
87C22⋊(C11⋊C8)—21no—
88#66885—22no—
89(C2×D11)⋊C8—21no—
90(C2×D11)⋊C8—21no—
91#66882—22no—
92#66881—22no—
93#66880—22no—
94#66879—21no—
95Dic11⋊C8—21no—
96Dic11⋊C8—21no—
97C8×Dic11—21no—
98#66874—22no—
99#66873—22no—
100#66872—22no—
101#66871—22no—
102#66871—22no—
103#66871—22no—
104#66871—22no—
105#66871—22no—
106C4⋊(C11⋊C8)C2312yes—
107#66867—21no—
108C4×C11⋊C8D411yescharacteristic
109C4×C11⋊C8D411yescharacteristic
110C4×C11⋊C8C2311yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112#19359—111nomaximal, Sylow
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—82no—
116C22×C4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—21no—
121C22×Dic11—41no—
122C2×D44C2×D411yescharacteristic
123C2×C4×D11—21no—
124C2×Dic22—22no—
125C2×Dic22—41no—
126C2×Dic22—82no—
127C2×Dic22C2×D411yescharacteristic
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138C42×C11C2411yescharacteristic
139C22⋊Dic11—21no—
140(C2×D11)⋊C4—21no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—21no—
143(C2×D11)⋊C4—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148C4⋊Dic11C2×D411yescharacteristic
149C4⋊Dic11C2×D411yescharacteristic
150Dic11⋊C4—21no—
151Dic11⋊C4—21no—
152Dic11⋊C4—21no—
153Dic11⋊C4—21no—
154C4×Dic11—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162#4313—42no—
163C8×D11—42no—
164#3238—111no—
165#3238—111no—
166C2×#500—111no—
167#2966—111no—
168#1696—112no—
169#1695—112no—
170#1676—112no—
171#1675—112no—
172#1568—111no—
173#1558—111no—
174#1558D1111yescharacteristic, complemented
175C23×C11#12111yescharacteristic
176C22×D11—21no—
177Q8×C11—82no—
178Q8×C11—82no—
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—42no—
184C2×C4×C11—82no—
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C22⋊D11—42no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—42no—
196C2×Dic11—82no—
197D44—22no—
198C4×D11—41no—
199C4×D11—41no—
200Dic22—22no—
201Dic22—82no—
202Dic22—82no—
203C8×C11—41no—
204C8×C11—41no—
205C8×C11—42no—
206C11⋊C8—21no—
207C11⋊C8—21no—
208C11⋊C8—42no—
209C11⋊C8#13712yes—
210C11⋊C8#13712yes—
211C2×C4⋊Q8—111no—
212C2×C4⋊Q8C2×D1111yescharacteristic
213#529—111no—
214#501—221no—
215#501—221no—
216#500—112no—
217#500—112no—
218#500—221no—
219#500—221no—
220#489—221no—
221#489—221no—
222#483—221no—
223#483—221no—
224#480—221no—
225#480—221no—
226#477—112no—
227#477—112no—
228#476—112no—
229#476—112no—
230#446—111no—
231C8×Q8—111no—
232#436—111no—
233#435—221no—
234C8×D4—111no—
235C8×D4—221no—
236#433—221no—
237#432—111no—
238#432C2×D1111yescharacteristic
239#432C2×D1111yescharacteristic
240C2×#107—221no—
241C2×#107—221no—
242#405—221no—
243C2×C4×C8—111no—
244#335—112no—
245#334—112no—
246#333—112no—
247#333—112no—
248#333C2×D1112yes—
249#333C2×D1112yes—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11#47212yes—
253C22×C11C2×#12111yescharacteristic
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—41no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—82no—
262C4×C11C2×#13711yescharacteristic
263C4×C11C2×#13711yescharacteristic
264C4×C11#57812yes—
265Dic11—41no—
266Dic11—41no—
267Dic11—41no—
268Dic11—82no—
269C22×Q8—21no—
270C22×Q8—221no—
271C2×M16—221no—
272C22×C8—111no—
273C22×C8—111no—
274C22×C8—221no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—112no—
279C4⋊Q8—221no—
280C4⋊Q8—221no—
281C4⋊Q8—221no—
282C4⋊Q8C22×D1112yes—
283#126—221no—
284#125—111no—
285#124—111no—
286#123—221no—
287C22⋊Q8—111no—
288#121—111no—
289C4×Q8—111no—
290C4×D4—111no—
291C4×D4—221no—
292#117—221no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—221no—
297C2×C42C22×D1111yescharacteristic
298#107—222no—
299#107—222no—
300#107—222no—
301#107—222no—
302#107—222no—
303#107—222no—
304#106—222no—
305#106—222no—
306C4⋊C8—112no—
307C4⋊C8—221no—
308C4⋊C8—221no—
309C4⋊C8C22×D1111yescharacteristic
310C4⋊C8C22×D1111yescharacteristic
311C4⋊C8C22×D1112yes—
312#103—222no—
313#103—222no—
314#102—222no—
315#102—222no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—221no—
319C22⋊C8—221no—
320C22⋊C8—221no—
321#97—21no—
322#97—21no—
323#97—221no—
324#97—221no—
325C4×C8—111no—
326C4×C8—111no—
327C4×C8—111no—
328C4×C8—111no—
329C4×C8—221no—
330C2×C11—22no—
331C2×C11#303911yescharacteristic
332C2×C11#305911yescharacteristic
333C2×C11C2×#47211yescharacteristic
334D11—81no—
335C2×Q8—22no—
336C2×Q8—41no—
337C2×Q8—82no—
338C2×Q8—111no—
339C2×Q8—222no—
340C2×Q8—441no—
341C2×Q8—882no—
342C2×D4—111no—
343C2×D4—221no—
344C22×C4—41no—
345C22×C4—221no—
346C22×C4—441no—
347C22×C4#433911yescharacteristic
348C22×C4D4×D1111yescharacteristic
349C22×C4D4×D1111yescharacteristic
350M16—442no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—22no—
354C2×C8—111no—
355C2×C8—111no—
356C2×C8—111no—
357C2×C8—111no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—442no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—111no—
367C4⋊C4—111no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C22⋊C4—221no—
377C22⋊C4—221no—
378C22⋊C4—221no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C42—221no—
382C42#433911yescharacteristic
383C42D4×D1111yescharacteristic
384C42D4×D1111yescharacteristic
385C42C23×D1111yescharacteristic
386C11#1935911yescharacteristic, complemented, Sylow
387C23—221no—
388C23#6693711yescharacteristic
389Q8—82no—
390Q8—82no—
391Q8—222no—
392Q8—882no—
393Q8—882no—
394D4—222no—
395D4—442no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—42no—
401C2×C4—82no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—442no—
408C2×C4—882no—
409C2×C4#6693711yescharacteristic
410C2×C4#6693711yescharacteristic
411C2×C4#6693711yescharacteristic
412C2×C4C2×#433911yescharacteristic
413C2×C4C2×D4×D1111yescharacteristic
414C2×C4C2×D4×D1111yescharacteristic
415C8—41no—
416C8—41no—
417C8—42no—
418C8—112no—
419C8—112no—
420C8—221no—
421C8—221no—
422C8—442no—
423C22—21no—
424C22—21no—
425C22—441no—
426C22—441no—
427C22—441no—
428C22#1062236212yes—
429C22C2×#6693711yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—82no—
435C4—441no—
436C4—441no—
437C4—441no—
438C4—882no—
439C4D11×#13711yescharacteristic
440C4D11×#13711yescharacteristic
441C4#1062331012yes—
442C2—22no—
443C2—881no—
444C2#1307810211yescharacteristic
445C2#1307827011yescharacteristic
446C2C2×#1062236211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1558C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#1558D11
hypocenterC11#19359
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
3. C2×#10622691C2semidirect
5. #13068143C2semidirect
6. #13068138C2semidirect
7. #13068019C2semidirect
8. #13068014C2semidirect
9. #13067377C2semidirect
10. #13067341C2semidirect
11. C11×#1558C2semidirect
174. #1558D11semidirect
386. C11#19359semidirect

Maximal subgroups

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

subgroupindex
#130798392
#130798372
C2×#106226912
#130775852
#130681432
#130681382
#130680192
#130680142
#130673772
#130673412
C11×#15582
#1935911