Finite Group Databasebeta

← #14775845

Subgroups — #14775845

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078398C211yesmaximal, characteristic
2#13077565C211yesmaximal, characteristic, complemented
3#13077185C211yesmaximal, characteristic
4#13069389C211yesmaximal, characteristic, complemented
5#13069363C212yesmaximal, complemented
6#13069213C212yesmaximal, complemented
7#13068892C212yesmaximal
8C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9#13068450C212yesmaximal
10C4×#66869C211yesmaximal, characteristic
11C11×#1994C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66960C2212yes—
14C4×#4339C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C43×C11C2211yescharacteristic
17C2×#66886C2212yes—
18#10622732C2212yes—
19#10622707C411yescharacteristic, complemented
20#10622704C411yescharacteristic, complemented
21#10622700C411yescharacteristic, complemented
22#10622697C411yescharacteristic, complemented
23#10622679C412yescomplemented
24#10622676C412yescomplemented
25#10622637—21no—
26#10622637—22no—
27Q8×C11⋊C8—21no—
28#10622615C2212yes—
29#10622612C2212yes—
30#10622611C2212yes—
31#10622610C2212yes—
32C2×#66869C2211yescharacteristic
33C2×#66869C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C4×#4318C2211yescharacteristic
37C2×C4×C11⋊C8C2212yes—
38#10622452—22no—
39#10622450—21no—
40D11×C4⋊C8—21no—
41C11×#339C2212yes—
42C11×#339C2212yes—
43#10622196C2212yes—
44#10622162C2212yes—
45#10622161C2211yescharacteristic
46#10622161C2211yescharacteristic
47C2×#4339C2311yescharacteristic
48C2×C11×M16C2312yes—
49C11×C4⋊Q8C2×C411yescharacteristic
50C11×C4⋊Q8C2×C411yescharacteristic
51C11×#125C2×C412yes—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C11×#117C2312yes—
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C4×C22⋊D11—21no—
63C4×C22⋊D11—21no—
64#66979C2311yescharacteristic
65C2×#4318C2311yescharacteristic
66C2×#4318C2311yescharacteristic
67C22×C11⋊C8C2312yes—
68C22×C11⋊C8C2312yes—
69#66960—24no—
70#66960—42no—
71C2×#4313—22no—
72C2×C8×D11—22no—
73C4×D44C2×C411yescharacteristic
74C4×D44C2×C411yescharacteristic
75#66925—21no—
76C42×D11—21no—
77C4×Dic22C2×C411yescharacteristic
78C4×Dic22C2×C411yescharacteristic
79C11×C4⋊C8—21no—
80C11×C4⋊C8—21no—
81#66886—42no—
82Dic11⋊C8—22no—
83Dic11⋊C8—22no—
84#66874C2×C412yes—
85#66874C2×C412yes—
86#66873C2×C412yes—
87#66873C2×C412yes—
88#66872C2×C412yes—
89#66872C2×C412yes—
90#66871C2×C412yes—
91#66871C2×C412yes—
92#66869—22no—
93#66869Q814yescomplemented
94C4⋊(C11⋊C8)—22no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)C2×C412yes—
97C4⋊(C11⋊C8)C2×C411yescharacteristic
98C4⋊(C11⋊C8)C2×C411yescharacteristic
99C4⋊(C11⋊C8)D411yescharacteristic
100C4⋊(C11⋊C8)D411yescharacteristic
101C4⋊(C11⋊C8)D412yes—
102#66867—21no—
103#66867—22no—
104C4×C11⋊C8—21no—
105C4×C11⋊C8—22no—
106C4×C11⋊C8—42no—
107#22982—111nomaximal, Sylow
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—21no—
116#4339—21no—
117#4339—21no—
118#4339C2×Q812yes—
119#4339#4112yes—
120C2×D44C22×C411yescharacteristic
121C2×C4×D11—21no—
122C2×C4×D11—21no—
123C2×C4×D11—21no—
124C2×Dic22C22×C411yescharacteristic
125C11×M16—22no—
126C11×M16—22no—
127C2×C8×C11—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4C22×C412yes—
133C11×C4⋊C4C22×C412yes—
134C11×C22⋊C4—22no—
135C42×C11—24no—
136C42×C11—22no—
137C42×C11—21no—
138C42×C11—21no—
139C42×C11—21no—
140C42×C11—42no—
141C42×C11C22×C411yescharacteristic
142C42×C11C22×C411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2×Q812yes—
146C22⋊Dic11—21no—
147(C2×D11)⋊C4—21no—
148(C2×D11)⋊C4—21no—
149C4⋊Dic11C22×C411yescharacteristic
150C4⋊Dic11C22×C411yescharacteristic
151Dic11⋊C4—21no—
152Dic11⋊C4—21no—
153C4×Dic11—21no—
154C4×Dic11—21no—
155C4×Dic11—21no—
156#4318—21no—
157#4318—21no—
158#4318—21no—
159#4318C2×Q812yes—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8C22×C412yes—
167C2×C11⋊C8C22×C412yes—
168C2×C11⋊C8C2×D412yes—
169C2×C11⋊C8C2×D412yes—
170#4313—44no—
171C8×D11—44no—
172#3076—111no—
173#2962—111no—
174#2906—111no—
175#1994D1111yescharacteristic, complemented
176#1950—111no—
177#1945—112no—
178#1922—112no—
179#1866—112no—
180C4×C4⋊C8—111no—
181#1764—112no—
182C4×#104—111no—
183C23×C11C2×#4111yescharacteristic
184C22×D11—21no—
185Q8×C11—42no—
186Q8×C11—81no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C4×D411yescharacteristic
198C2×C4×C11C4×D411yescharacteristic
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11C4×D411yescharacteristic
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×Q811yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C22⋊D11—22no—
208C22⋊D11—22no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212D44—21no—
213D44C4×Q812yes—
214C4×D11—22no—
215C4×D11—22no—
216C4×D11—42no—
217C4×D11—81no—
218Dic22—21no—
219Dic22C4×Q812yes—
220C8×C11—42no—
221C11⋊C8—22no—
222C11⋊C8—22no—
223C11⋊C8—22no—
224C11⋊C8—22no—
225C11⋊C8—22no—
226C11⋊C8—41no—
227C2×#131—112no—
228#533C2×D1111yescharacteristic
229C4×#41—111no—
230#479—112no—
231#478—112no—
232#477—111no—
233#476—111no—
234#475—111no—
235#474—111no—
236#446—222no—
237#446—221no—
238C8×Q8—221no—
239C2×#108—112no—
240#427—112no—
241#424—112no—
242#424—112no—
243#424—222no—
244#423—221no—
245#423C2×D1111yescharacteristic
246C2×C4⋊C8—111no—
247C2×C4⋊C8—111no—
248C2×C4⋊C8—221no—
249C2×#104—111no—
250C2×#104—111no—
251#416—112no—
252#405—112no—
253C4×M16—111no—
254C2×C4×C8—112no—
255C43C2×D1111yescharacteristic
256#341—112no—
257#339—111no—
258#339—111no—
259#339C2×D1112yes—
260#339C2×D1112yes—
261#336—112no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11C2×C4×D411yescharacteristic
265C22×C11#55211yescharacteristic
266C22×C11#55411yescharacteristic
267C2×D11—22no—
268C2×D11—41no—
269C2×D11—41no—
270C4×C11—24no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11#44312yes—
278C4×C11C2×C4×Q811yescharacteristic
279C4×C11#52011yescharacteristic
280C4×C11#54611yescharacteristic
281C4×C11D4×Q811yescharacteristic
282Dic11—22no—
283Dic11—41no—
284Dic11—41no—
285C2×#41—111no—
286#131—224no—
287#131—442no—
288C2×M16—111no—
289C2×M16—111no—
290C2×M16—222no—
291C2×M16C22×D1112yes—
292C22×C8—112no—
293C22×C8—112no—
294C22×C8—222no—
295C4⋊Q8C4×D1111yescharacteristic
296C4⋊Q8C4×D1111yescharacteristic
297#125C4×D1112yes—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—111no—
303C4×Q8—111no—
304C4×D4—111no—
305C4×D4—111no—
306C4×D4—221no—
307C4×D4—221no—
308#117—111no—
309#117—221no—
310#117C22×D1112yes—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—221no—
314C2×C42C22×D1111yescharacteristic
315C2×C42C22×D1111yescharacteristic
316C2×C42C22×D1111yescharacteristic
317#108—442no—
318#107—112no—
319#107—112no—
320#106—112no—
321#106—112no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8—111no—
325C4⋊C8—111no—
326C4⋊C8—112no—
327C4⋊C8—111no—
328C4⋊C8—111no—
329C4⋊C8—112no—
330C4⋊C8—222no—
331C4⋊C8—222no—
332C4⋊C8—222no—
333C4⋊C8—222no—
334#104—114no—
335#104—222no—
336#103—112no—
337#103—112no—
338#102—112no—
339#102—112no—
340#97—222no—
341#97—221no—
342C4×C8—222no—
343C4×C8—221no—
344C4×C8—442no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11#236011yescharacteristic
348C2×C11C2×#44311yescharacteristic
349C2×C11#295611yescharacteristic
350D11—42no—
351#41—112no—
352#41—112no—
353#41—221no—
354#41—221no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—111no—
358C2×D4—111no—
359C2×D4—221no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4#434111yescharacteristic
366C22×C4#434111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368M16—22no—
369M16—22no—
370M16—112no—
371M16—221no—
372M16—221no—
373M16—221no—
374M16—444no—
375C2×C8—22no—
376C2×C8—112no—
377C2×C8—112no—
378C2×C8—112no—
379C2×C8—112no—
380C2×C8—221no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—222no—
385C2×C8—221no—
386C2×C8—444no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—111no—
392C4⋊C4—111no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4C2×C4×D1112yes—
396C4⋊C4C2×C4×D1112yes—
397C22⋊C4—22no—
398C22⋊C4—221no—
399C22⋊C4—221no—
400C22⋊C4—221no—
401C42—24no—
402C42—22no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42—42no—
407C42—221no—
408C42—221no—
409C42—221no—
410C42C2×C4×D1111yescharacteristic
411C42C2×C4×D1111yescharacteristic
412C42D4×D1111yescharacteristic
413C42D4×D1111yescharacteristic
414C42Q8×D1112yes—
415C11#2298211yescharacteristic, complemented, Sylow
416C23—221no—
417C23C2×#434111yescharacteristic
418Q8—42no—
419Q8—81no—
420Q8—112no—
421Q8—221no—
422D4—112no—
423D4—222no—
424D4—222no—
425D4—221no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—221no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—442no—
442C2×C4—881no—
443C2×C4(C22⋊D11)⋊C411yescharacteristic
444C2×C4(C22⋊D11)⋊C411yescharacteristic
445C2×C4(C22⋊D11)⋊C411yescharacteristic
446C2×C4(C22⋊D11)⋊C411yescharacteristic
447C2×C4C22×C4×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4C2×Q8×D1111yescharacteristic
450C2×C4#6704011yescharacteristic
451C2×C4#41×D1111yescharacteristic
452C2×C4#6704211yescharacteristic
453C8—42no—
454C8—222no—
455C8—222no—
456C8—222no—
457C8—222no—
458C8—222no—
459C8—441no—
460C22—21no—
461C22—21no—
462C22—222no—
463C22—441no—
464C22—441no—
465C22C2×(C22⋊D11)⋊C411yescharacteristic
466C22#1062316611yescharacteristic
467C22#1062317011yescharacteristic
468C4—24no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—222no—
476C4—441no—
477C4—441no—
478C4#1062243712yes—
479C4C4×Q8×D1111yescharacteristic
480C4#1062310511yescharacteristic
481C4#1062320711yescharacteristic
482C4#1062325811yescharacteristic
483C2—21no—
484C2—21no—
485C2—442no—
486C2#1307162611yescharacteristic
487C2C2×#1062243711yescharacteristic
488C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1994C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#1994D11
hypocenterC11#22982
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
2. #13077565C2semidirect
4. #13069389C2semidirect
5. #13069363C2semidirect
6. #13069213C2semidirect
8. C4×C4⋊(C11⋊C8)C2semidirect
11. C11×#1994C2semidirect
19. #10622707C4semidirect
20. #10622704C4semidirect
21. #10622700C4semidirect
22. #10622697C4semidirect
23. #10622679C4semidirect
24. #10622676C4semidirect
93. #66869Q8semidirect
175. #1994D11semidirect
415. C11#22982semidirect

Maximal subgroups

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

subgroupindex
#130783982
#130775652
#130771852
#130693892
#130693632
#130692132
#130688922
C4×C4⋊(C11⋊C8)2
#130684502
C4×#668692
C11×#19942
#2298211