Finite Group Databasebeta

← #14737413

Subgroups — #14737413

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13068200C212yesmaximal, complemented
5#13068158C212yesmaximal, complemented
6#13068076C212yesmaximal, complemented
7#13068034C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9C2×#10622184C211yesmaximal, characteristic, complemented
10#13067263C211yesmaximal, characteristic
11C11×#3230C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#500—21no—
16C11×#487—21no—
17C11×#484—22no—
18C11×#477C2212yes—
19C11×#477C2212yes—
20C11×#431C2211yescharacteristic
21#10622706C2212yes—
22#10622702—22no—
23#10622701C2212yes—
24#10622697—21no—
25#10622696—21no—
26#10622661—22no—
27#10622640C2212yes—
28#10622637—22no—
29#10622637C2212yes—
30Q8×C11⋊C8C2212yes—
31#10622633C2212yes—
32#10622612—21no—
33#10622610—21no—
34#10622579—21no—
35#10622579—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622184C2212yes—
40#10622184C2212yes—
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×#4325—22no—
65#66983—21no—
66#66983—21no—
67C2×#4318D411yescharacteristic
68C2×#4318D411yescharacteristic
69C22×C11⋊C8—21no—
70C22×C11⋊C8—21no—
71#66928—21no—
72#66927C2311yescharacteristic
73C4×D44—21no—
74C4×D44—21no—
75#66922C2311yescharacteristic
76C11×#107—22no—
77C11×#107—22no—
78C11×C4⋊C8C2311yescharacteristic
79C11×C4⋊C8C2311yescharacteristic
80C11×#103—22no—
81C11×#103—22no—
82C11×C22⋊C8—21no—
83C4×C8×C11—21no—
84#66899—22no—
85#66874—22no—
86#66874—22no—
87#66873—22no—
88#66873—22no—
89#66873—22no—
90#66872—22no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)—21no—
93C4⋊(C11⋊C8)—22no—
94C4⋊(C11⋊C8)—22no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98#66867—22no—
99#66867D412yes—
100C4×C11⋊C8—22no—
101C4×C11⋊C8C2312yes—
102#19244—111nomaximal, Sylow
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—41no—
106C2×Q8×C11—82no—
107C2×Q8×C11C2×D412yes—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C2×C22⋊D11—41no—
113#4339—42no—
114#4339—42no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×C4×D11—41no—
119C2×Dic22—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4C2×D412yes—
132C11×C22⋊C4—22no—
133C42×C11—22no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138#4325—82no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143#4318—22no—
144#4318—22no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—42no—
149C2×C11⋊C8—81no—
150C2×C11⋊C8C2×D412yes—
151C2×C11⋊C8C2×D412yes—
152#3246—111no—
153#3230D1111yescharacteristic, complemented
154#3141—111no—
155#2962—111no—
156#1704—112no—
157#1698—112no—
158#1684—112no—
159#1678—112no—
160#1565—111no—
161C2×#333—111no—
162#1540—111no—
163C23×C11#12111yescharacteristic
164C22×D11—41no—
165Q8×C11—22no—
166Q8×C11—22no—
167Q8×C11—81no—
168Q8×C11—82no—
169Q8×C11—82no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—82no—
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#13512yes—
181C2×C4×C11#13712yes—
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C22⋊D11—82no—
186C2×Dic11—41no—
187D44—41no—
188D44—41no—
189D44—41no—
190D44—41no—
191D44—81no—
192C4×D11—82no—
193Dic22—41no—
194Dic22—41no—
195C8×C11—41no—
196C8×C11—41no—
197C11⋊C8—22no—
198C11⋊C8—22no—
199C11⋊C8—41no—
200C11⋊C8—41no—
201C11⋊C8—42no—
202#533C2×D1111yescharacteristic
203#532—111no—
204C2×C4⋊Q8C2×D1111yescharacteristic
205#500—21no—
206#489—222no—
207#487—21no—
208#487—112no—
209#486—112no—
210#484—22no—
211#477C2×D1112yes—
212#477C2×D1112yes—
213#476—221no—
214#475—112no—
215#465—222no—
216#461—221no—
217#460—112no—
218#446—112no—
219#446—222no—
220C8×Q8—112no—
221#431C2×D1111yescharacteristic
222#424—221no—
223C2×C4⋊C8—111no—
224C2×C4⋊C8—111no—
225#417—221no—
226#417—221no—
227#405—221no—
228C4×M16—111no—
229#335—112no—
230#334—112no—
231#333—112no—
232#333—112no—
233#332—111no—
234#332—111no—
235#331—111no—
236#331—111no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11#46412yes—
240C22×C11C2×#12111yescharacteristic
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—82no—
250C4×C11#46412yes—
251C4×C11C2×#13511yescharacteristic
252C4×C11C2×#13711yescharacteristic
253C4×C11#57711yescharacteristic
254C4×C11#57811yescharacteristic
255Dic11—81no—
256C2×#41—221no—
257C22×Q8—21no—
258C2×SD16—222no—
259C2×M16—111no—
260C2×M16—111no—
261C22×C8—221no—
262C22×C8—221no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—111no—
267C4⋊Q8C22⋊D1111yescharacteristic
268C4⋊Q8C22⋊D1111yescharacteristic
269C4⋊Q8C22×D1112yes—
270#127—111no—
271#125—21no—
272#124—221no—
273C22⋊Q8—21no—
274C22⋊Q8C22⋊D1112yes—
275#121—221no—
276#121—221no—
277C4×Q8—21no—
278C4×Q8C22×D1112yes—
279C4×D4—221no—
280C4×D4—221no—
281#117—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C42C22×D1111yescharacteristic
285#107—22no—
286#107—22no—
287#106—222no—
288C4⋊C8—111no—
289C4⋊C8—111no—
290C4⋊C8—112no—
291C4⋊C8—222no—
292C4⋊C8—222no—
293C4⋊C8—221no—
294C4⋊C8—221no—
295C4⋊C8C22×D1111yescharacteristic
296C4⋊C8C22×D1111yescharacteristic
297#103—22no—
298#103—22no—
299#103—222no—
300#103—222no—
301#103—222no—
302#102—222no—
303#102—222no—
304#102—222no—
305C22⋊C8—21no—
306#97—112no—
307#97—222no—
308C4×C8—21no—
309C4×C8—112no—
310C4×C8—222no—
311C2×C11—22no—
312C2×C11C2×#46411yescharacteristic
313C2×C11#306311yescharacteristic
314C2×C11#306811yescharacteristic
315D11—161no—
316#41—442no—
317#41—442no—
318C2×Q8—21no—
319C2×Q8—22no—
320C2×Q8—41no—
321C2×Q8—82no—
322C2×Q8—221no—
323C2×Q8C2×C22⋊D1112yes—
324C2×D4—221no—
325C2×D4—221no—
326C2×D4—221no—
327C2×D4—441no—
328C22×C4—41no—
329C22×C4—441no—
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—882no—
334M16—222no—
335M16—222no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—112no—
339C2×C8—112no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—222no—
343C2×C8—442no—
344C2×C8—881no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—221no—
355C4⋊C4—221no—
356C4⋊C4C2×C22⋊D1112yes—
357C22⋊C4—22no—
358C22⋊C4—441no—
359C22⋊C4—441no—
360C42—22no—
361C42D4×D1111yescharacteristic
362C42#434111yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C42C23×D1111yescharacteristic
365C11#1924411yescharacteristic, complemented, Sylow
366C23—441no—
367C23#6699211yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—81no—
371Q8—82no—
372Q8—82no—
373Q8—441no—
374Q8—441no—
375D4—441no—
376D4—441no—
377D4—441no—
378D4—441no—
379D4—881no—
380D4—882no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—82no—
388C2×C4—441no—
389C2×C4—882no—
390C2×C4#6697112yes—
391C2×C4#6697212yes—
392C2×C4#6699211yescharacteristic
393C2×C4#6699211yescharacteristic
394C2×C4#6699211yescharacteristic
395C2×C4C2×D4×D1111yescharacteristic
396C2×C4C2×#434111yescharacteristic
397C2×C4C22×C22⋊D1111yescharacteristic
398C8—41no—
399C8—41no—
400C8—222no—
401C8—222no—
402C8—441no—
403C8—441no—
404C8—442no—
405C22—21no—
406C22—21no—
407C22—881no—
408C22—881no—
409C22—881no—
410C22#1062279812yes—
411C22C2×#6699211yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—42no—
417C4—82no—
418C4—881no—
419C4#1062279812yes—
420C4C2×#6697111yescharacteristic
421C4C2×#6697211yescharacteristic
422C4#1062336811yescharacteristic
423C4#1062336911yescharacteristic
424C2—22no—
425C2—1761no—
426C2C2×#1062279811yescharacteristic
427C2#1307830311yescharacteristic
428C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3230C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3230D11
hypocenterC11#19244
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
3. #13077565C2semidirect
4. #13068200C2semidirect
5. #13068158C2semidirect
6. #13068076C2semidirect
7. #13068034C2semidirect
8. #13067369C2semidirect
9. C2×#10622184C2semidirect
11. C11×#3230C2semidirect
153. #3230D11semidirect
365. C11#19244semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130790122
#130775652
#130682002
#130681582
#130680762
#130680342
#130673692
C2×#106221842
#130672632
C11×#32302
#1924411