Finite Group Databasebeta

← #14738571

Subgroups — #14738571

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079839C211yesmaximal, characteristic
2#13079645C211yesmaximal, characteristic
3C2×#10622293C211yesmaximal, characteristic, complemented
4#13077591C211yesmaximal, characteristic
5#13068123C212yesmaximal, complemented
6#13068116C212yesmaximal, complemented
7#13067999C212yesmaximal, complemented
8#13067992C212yesmaximal, complemented
9#13067341C211yesmaximal, characteristic, complemented
10#13067334C211yesmaximal, characteristic, complemented
11C11×#1568C211yesmaximal, characteristic, complemented
12#10623010C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C11×#432C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622724—21no—
19C8×C22⋊D11—21no—
20C2×#66881—21no—
21C2×#66881—21no—
22#10622539C2211yescharacteristic
23#10622463C2212yes—
24#10622462C2212yes—
25#10622455C2212yes—
26#10622454C2212yes—
27#10622352—21no—
28#10622351—21no—
29#10622349—21no—
30#10622334—21no—
31#10622328—21no—
32#10622327—21no—
33#10622316—21no—
34#10622315—21no—
35#10622303—21no—
36#10622302—21no—
37#10622301C2211yescharacteristic
38C8×D44C2211yescharacteristic
39#10622293—21no—
40#10622293—21no—
41#10622293C2212yes—
42#10622293C2212yes—
43#10622292C2211yescharacteristic
44C8×Dic22C2211yescharacteristic
45C11×#335C2212yes—
46C11×#334C2212yes—
47#10622120C2212yes—
48#10622120C2212yes—
49#10622119C2212yes—
50#10622119C2212yes—
51C22×Dic22—21no—
52C22×Dic22—21no—
53C22×C8×C11D411yescharacteristic
54C22×C8×C11D411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56#66983D411yescharacteristic
57#66982—21no—
58C4×C22⋊D11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63#66977D411yescharacteristic
64C2×Dic44—22no—
65C2×#4314—22no—
66C2×#4313—21no—
67C2×C8×D11—21no—
68#66929—21no—
69#66928D411yescharacteristic
70C4×D44C2311yescharacteristic
71#66925—21no—
72#66923D411yescharacteristic
73#66922—21no—
74#66922—21no—
75#66922—21no—
76#66922—21no—
77#66922—21no—
78#66922—21no—
79#66922C2312yes—
80#66922C2312yes—
81C4×Dic22C2311yescharacteristic
82C11×C4⋊C8C2312yes—
83C11×C4⋊C8C2312yes—
84C11×C22⋊C8—21no—
85C11×C22⋊C8—21no—
86C11×#97—21no—
87C11×#97—21no—
88C4×C8×C11D411yescharacteristic
89C4×C8×C11D411yescharacteristic
90C4×C8×C11C2311yescharacteristic
91C4×C8×C11C2311yescharacteristic
92C22⋊(C11⋊C8)—21no—
93#66885—22no—
94(C2×D11)⋊C8—21no—
95(C2×D11)⋊C8—21no—
96#66882—22no—
97#66881—22no—
98#66881—22no—
99#66881—22no—
100#66881—22no—
101#66881—22no—
102#66880—22no—
103#66880—22no—
104#66880—22no—
105#66879—21no—
106Dic11⋊C8—21no—
107Dic11⋊C8—21no—
108C8×Dic11—21no—
109C4⋊(C11⋊C8)C2311yescharacteristic
110C4⋊(C11⋊C8)C2311yescharacteristic
111#66867—21no—
112#19357—111nomaximal, Sylow
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C2×C22⋊D11—21no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C2×D44C2×D411yescharacteristic
120C2×C4×D11—21no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22—41no—
124C2×Dic22—41no—
125C2×Dic22—82no—
126C2×Dic22—82no—
127C2×Dic22C2×D411yescharacteristic
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140C22⋊Dic11—21no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—21no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11C2×D411yescharacteristic
154C4⋊Dic11C2×D411yescharacteristic
155Dic11⋊C4—21no—
156Dic11⋊C4—21no—
157Dic11⋊C4—21no—
158Dic11⋊C4—21no—
159C4×Dic11—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162Dic44—82no—
163#4314—82no—
164#4313—42no—
165C8×D11—42no—
166#3238—111no—
167#3218—111no—
168C2×#498—111no—
169#2966—111no—
170#1692—112no—
171#1691—112no—
172#1672—112no—
173#1671—112no—
174#1568D1111yescharacteristic, complemented
175#1558—111no—
176#1556—111no—
177C23×C11#12111yescharacteristic
178C22×D11—21no—
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C22⋊D11—42no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—82no—
196C2×Dic11—82no—
197D44—22no—
198C4×D11—41no—
199C4×D11—41no—
200Dic22—22no—
201Dic22—42no—
202Dic22—42no—
203Dic22—82no—
204Dic22—82no—
205Dic22—82no—
206C8×C11—21no—
207C8×C11—21no—
208C8×C11—42no—
209C8×C11—42no—
210C8×C11#13712yes—
211C8×C11#13712yes—
212C11⋊C8—41no—
213C11⋊C8—41no—
214C2×C4⋊Q8—111no—
215C2×C4⋊Q8—111no—
216#529—111no—
217#501—221no—
218#498—112no—
219#498—112no—
220#498—221no—
221#498—221no—
222#497—221no—
223#491—221no—
224#489—221no—
225#483—221no—
226#480—221no—
227#477—112no—
228#476—112no—
229#462—112no—
230#461—112no—
231#451—221no—
232#448—221no—
233#446—111no—
234C8×Q8—111no—
235#436—111no—
236#435—221no—
237C8×D4—111no—
238C8×D4—221no—
239#433—221no—
240#432—111no—
241#432C2×D1111yescharacteristic
242#432C2×D1111yescharacteristic
243C2×#106—221no—
244C2×#106—221no—
245#405—221no—
246C2×C4×C8C2×D1111yescharacteristic
247#335C2×D1112yes—
248#334C2×D1112yes—
249#333—112no—
250#333—112no—
251#332—112no—
252#332—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11#47112yes—
256C22×C11C2×#12111yescharacteristic
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—41no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11C2×#13711yescharacteristic
265C4×C11C2×#13711yescharacteristic
266C4×C11#57712yes—
267Dic11—41no—
268Dic11—41no—
269Dic11—41no—
270Dic11—82no—
271Dic11—82no—
272C22×Q8—221no—
273C22×Q8—221no—
274C2×Q16—222no—
275C2×SD16—222no—
276C2×M16—221no—
277C22×C8—221no—
278C22×C8D4411yescharacteristic
279C22×C8D4411yescharacteristic
280C4⋊Q8—112no—
281C4⋊Q8—112no—
282C4⋊Q8—221no—
283C4⋊Q8—221no—
284C4⋊Q8—221no—
285C4⋊Q8—221no—
286C4⋊Q8—221no—
287C4⋊Q8—221no—
288#126—221no—
289#125—111no—
290#124—111no—
291#123—221no—
292C22⋊Q8—111no—
293#121—111no—
294C4×Q8—111no—
295C4×D4—111no—
296C4×D4—221no—
297#117—221no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C42C22×D1111yescharacteristic
303#107—222no—
304#106—222no—
305#106—222no—
306#106—222no—
307#106—222no—
308#106—222no—
309C4⋊C8—111no—
310C4⋊C8—111no—
311C4⋊C8—221no—
312C4⋊C8—221no—
313C4⋊C8C22×D1112yes—
314C4⋊C8C22×D1112yes—
315#103—222no—
316#103—222no—
317#103—222no—
318#102—222no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—221no—
322C22⋊C8—221no—
323C22⋊C8—221no—
324#97—21no—
325#97—21no—
326#97—221no—
327#97—221no—
328C4×C8—221no—
329C4×C8D4411yescharacteristic
330C4×C8D4411yescharacteristic
331C4×C8C22×D1111yescharacteristic
332C4×C8C22×D1111yescharacteristic
333C2×C11—22no—
334C2×C11#303911yescharacteristic
335C2×C11#305711yescharacteristic
336C2×C11C2×#47111yescharacteristic
337D11—81no—
338C2×Q8—111no—
339C2×Q8—222no—
340C2×Q8—222no—
341C2×Q8—441no—
342C2×Q8—441no—
343C2×Q8—882no—
344C2×Q8—882no—
345C2×D4—111no—
346C2×D4—221no—
347C22×C4—221no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4C2×D4411yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4#434311yescharacteristic
353Q16—882no—
354SD16—882no—
355M16—442no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—221no—
361C2×C8—221no—
362C2×C8—442no—
363C2×C8C2×D4411yescharacteristic
364C2×C8C2×D4411yescharacteristic
365C2×C8C2×D4411yescharacteristic
366C2×C8C2×D4411yescharacteristic
367C4⋊C4—111no—
368C4⋊C4—111no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C22⋊C4—221no—
382C22⋊C4—221no—
383C22⋊C4—221no—
384C22⋊C4—221no—
385C22⋊C4—221no—
386C42—221no—
387C42C2×D4411yescharacteristic
388C42D4×D1111yescharacteristic
389C42#434311yescharacteristic
390C42C23×D1111yescharacteristic
391C11#1935711yescharacteristic, complemented, Sylow
392C23—221no—
393C23#6694811yescharacteristic
394Q8—222no—
395Q8—442no—
396Q8—442no—
397Q8—882no—
398Q8—882no—
399Q8—882no—
400D4—222no—
401D4—442no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—882no—
414C2×C4—882no—
415C2×C4#6694811yescharacteristic
416C2×C4#6694811yescharacteristic
417C2×C4#6694811yescharacteristic
418C2×C4C22×D4411yescharacteristic
419C2×C4C2×D4×D1111yescharacteristic
420C2×C4C2×#434311yescharacteristic
421C8—21no—
422C8—21no—
423C8—42no—
424C8—42no—
425C8—441no—
426C8—441no—
427C8#6696212yes—
428C8#6696212yes—
429C22—21no—
430C22—21no—
431C22—441no—
432C22—441no—
433C22—441no—
434C22#1062251112yes—
435C22C2×#6694811yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—441no—
441C4—441no—
442C4—441no—
443C4—882no—
444C4—882no—
445C4C2×#6696211yescharacteristic
446C4C2×#6696211yescharacteristic
447C4#1062330112yes—
448C2—22no—
449C2—881no—
450C2#1307810411yescharacteristic
451C2#1307825611yescharacteristic
452C2C2×#1062251111yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1568C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#1568D11
hypocenterC11#19357
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
3. C2×#10622293C2semidirect
5. #13068123C2semidirect
6. #13068116C2semidirect
7. #13067999C2semidirect
8. #13067992C2semidirect
9. #13067341C2semidirect
10. #13067334C2semidirect
11. C11×#1568C2semidirect
174. #1568D11semidirect
391. C11#19357semidirect

Maximal subgroups

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

subgroupindex
#130798392
#130796452
C2×#106222932
#130775912
#130681232
#130681162
#130679992
#130679922
#130673412
#130673342
C11×#15682
#1935711