Finite Group Databasebeta

← #14909404

Subgroups — #14909404

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079271C211yesmaximal, characteristic, complemented
2#13079262C211yesmaximal, characteristic
3#13070894C211yesmaximal, characteristic, complemented
4#13070870C211yesmaximal, characteristic, complemented
5#13070860C211yesmaximal, characteristic, complemented
6#13070856C211yesmaximal, characteristic, complemented
7#13070732C211yesmaximal, characteristic, complemented
8#13070728C211yesmaximal, characteristic, complemented
9#13070713C211yesmaximal, characteristic, complemented
10#13070709C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070478C211yesmaximal, characteristic, complemented
13C4×#66864C211yesmaximal, characteristic, complemented
14#13070211C211yesmaximal, characteristic, complemented
15C4×C11×SD32C211yesmaximal, characteristic, complemented
16#10623114—21no—
17#10623093—21no—
18C2×C11×SD32C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21#10622801C2211yescharacteristic
22#10622794C2211yescharacteristic
23C2×#66892C2211yescharacteristic
24#10622770C2211yescharacteristic
25#10622764C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27#10622643—21no—
28#10622627—21no—
29C2×#66864C2211yescharacteristic
30C2×#66862C2211yescharacteristic
31C2×C16×D11C2211yescharacteristic
32#10622500C2211yescharacteristic
33#10622496C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622491C2211yescharacteristic
36#10622429—21no—
37#10622410—21no—
38#10622395—21no—
39#10622377—21no—
40C4×Dic44C2211yescharacteristic
41C4×D88C2211yescharacteristic
42#10622302C2211yescharacteristic
43C11×#367C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C4×C11×C16C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622140C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C4×Q8×C11—21no—
62C4×D4×C11—21no—
63#66999—21no—
64#66997—21no—
65C2×#4326—21no—
66#66993—21no—
67#66991—21no—
68C2×#4323—21no—
69#66983—41no—
70#66982—41no—
71C2×Dic44C2311yescharacteristic
72C2×D88C2311yescharacteristic
73C2×#4313D411yescharacteristic
74C2×C8×D11C2311yescharacteristic
75#66951—41no—
76#66950—21no—
77#66948—21no—
78#66943—21no—
79#66943—21no—
80#66942—41no—
81#66937—41no—
82#66936—41no—
83#66929—41no—
84C4×D44—21no—
85#66925D411yescharacteristic
86#66923—41no—
87C4×Dic22—21no—
88C11×SD32—22no—
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#103—21no—
94C11×#102—21no—
95C4×C8×C11C2311yescharacteristic
96#66899—21no—
97#66896—21no—
98#66892—22no—
99#66891—22no—
100#66885—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66880—21no—
104#66879D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66873—21no—
110#66872—21no—
111#66872—21no—
112#66867D411yescharacteristic
113#66864—22no—
114#66862—22no—
115C16×D11—22no—
116#33743—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×D44—21no—
124C2×D44—41no—
125C2×C4×D11—41no—
126C2×C4×D11C2×D411yescharacteristic
127C2×Dic22—21no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11—41no—
139C42×C11C2×D411yescharacteristic
140C22⋊Dic11—41no—
141#4326—42no—
142#4323—42no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4D811yescharacteristic
148(C2×D11)⋊C4D811yescharacteristic
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4D811yescharacteristic
161Dic11⋊C4D811yescharacteristic
162C4×Dic11—41no—
163C4×Dic11C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166Dic44—21no—
167Dic44—21no—
168D88—21no—
169D88—21no—
170#4313—22no—
171C8×D11—21no—
172C8×D11—21no—
173C11×C16—21no—
174C11×C16#4112yes—
175C11⋊C16—21no—
176C11⋊C16#4112yes—
177#3177—111no—
178#3176—111no—
179#2253—111no—
180#2248—111no—
181#2245—111no—
182#2244—111no—
183#2220—111no—
184#2220—111no—
185#2217—111no—
186#2217—111no—
187#2175—111no—
188#2175—111no—
189C4×SD32—111no—
190C4×SD32D1111yescharacteristic, complemented
191#2108—111no—
192C23×C11—41no—
193C22×D11—41no—
194C22×D11C2×D811yescharacteristic
195Q8×C11—41no—
196Q8×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—161no—
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C22⋊D11—161no—
207C22⋊D11—161no—
208C22⋊D11—161no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215D44—41no—
216D44—41no—
217D44—161no—
218C4×D11—21no—
219C4×D11—21no—
220C4×D11—161no—
221Dic22—41no—
222Dic22—41no—
223C8×C11—21no—
224C8×C11C2×#4111yescharacteristic
225C8×C11C2×#4111yescharacteristic
226C11⋊C8—21no—
227C11⋊C8#13512yes—
228#541—221no—
229#540—221no—
230C2×SD32—111no—
231C2×SD32—111no—
232C2×SD32—111no—
233C2×SD32C2×D1111yescharacteristic
234C2×M32—111no—
235C22×C16—111no—
236#499—111no—
237#499—111no—
238#494—111no—
239#493—111no—
240#491—221no—
241#490—221no—
242#470—221no—
243#469—221no—
244#467—111no—
245#467—111no—
246#466—111no—
247#466—111no—
248#442—221no—
249#441—221no—
250C4×Q16—111no—
251C4×Q16C2×D1111yescharacteristic
252C4×D8—111no—
253C4×D8C2×D1111yescharacteristic
254#405—111no—
255#367—111no—
256#367C2×D1111yescharacteristic
257#366—111no—
258#366—111no—
259#358—111no—
260#358—111no—
261#358—111no—
262#358C2×D1111yescharacteristic
263#357—111no—
264#357—111no—
265#357—111no—
266#357C2×D1111yescharacteristic
267#346—111no—
268#346—111no—
269C4×C16—111no—
270C4×C16C2×D1111yescharacteristic
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11C22×D811yescharacteristic
275C2×D11—21no—
276C2×D11—21no—
277C2×D11—21no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11#53211yescharacteristic
287C4×C11C2×#13511yescharacteristic
288Dic11—21no—
289Dic11—21no—
290Dic11—21no—
291Dic11—81no—
292Dic11—81no—
293Dic11—81no—
294C2×Q16—111no—
295C2×Q16—221no—
296C2×Q16C22×D1111yescharacteristic
297C2×D8—111no—
298C2×D8—221no—
299C2×D8C22×D1111yescharacteristic
300C2×M16—111no—
301C22×C8—111no—
302C4⋊Q8—221no—
303#127—221no—
304#126—441no—
305#126—441no—
306#125—221no—
307#125—221no—
308#125—441no—
309#125—441no—
310#123—441no—
311#123—441no—
312C22⋊Q8—221no—
313C22⋊Q8—221no—
314#121—221no—
315#121—221no—
316#121—441no—
317#121—441no—
318C4×Q8—21no—
319C4×Q8—221no—
320C4×D4—21no—
321C4×D4—221no—
322#117—111no—
323SD32—22no—
324SD32—222no—
325SD32—222no—
326SD32—222no—
327M32—222no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16—222no—
331C2×C16C22×D1111yescharacteristic
332C2×C16C22×D1111yescharacteristic
333#107—111no—
334#107—111no—
335#107C22×D1111yescharacteristic
336#107C22×D1111yescharacteristic
337#106—221no—
338#106—221no—
339#103—21no—
340#103—221no—
341#103—221no—
342#103—221no—
343#102—21no—
344#102—221no—
345#102—221no—
346#102—221no—
347#97—111no—
348#97—111no—
349C4×C8—111no—
350C4×C8C22×D1111yescharacteristic
351C2×C11—161no—
352C2×C11#316911yescharacteristic
353C2×C11#341611yescharacteristic
354C2×C11#341611yescharacteristic
355D11—41no—
356D11—161no—
357C2×Q8—21no—
358C2×Q8—221no—
359C2×D4—21no—
360C2×D4—221no—
361C2×D4—441no—
362C2×D4—441no—
363C2×D4—441no—
364C2×D4—441no—
365C22×C4—41no—
366C22×C4—111no—
367C22×C4—441no—
368Q16—21no—
369Q16—21no—
370Q16—221no—
371Q16—221no—
372Q16—442no—
373D8—21no—
374D8—21no—
375D8—221no—
376D8—221no—
377D8—442no—
378M16—222no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8D4×D1111yescharacteristic
384C2×C8C23×D1111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—111no—
389C4⋊C4—111no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C22⋊C4—41no—
402C22⋊C4—111no—
403C22⋊C4—111no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C42—41no—
410C42—111no—
411C42—441no—
412C42D4×D1111yescharacteristic
413C16—21no—
414C16—112no—
415C16—221no—
416C16#433912yes—
417C11#3374311yescharacteristic, complemented, Sylow
418C23—41no—
419C23—111no—
420C23—441no—
421Q8—41no—
422Q8—41no—
423Q8—441no—
424Q8—441no—
425D4—41no—
426D4—41no—
427D4—441no—
428D4—441no—
429D4—1761no—
430D4—1761no—
431D4—1761no—
432D4—1761no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—111no—
439C2×C4—161no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—1761no—
446C2×C4D8×D1111yescharacteristic
447C2×C4D8×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C8—21no—
450C8—112no—
451C8—221no—
452C8C2×#433911yescharacteristic
453C8#41×D1111yescharacteristic
454C22—81no—
455C22—81no—
456C22—81no—
457C22—221no—
458C22—221no—
459C22—221no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—221no—
470C4—221no—
471C4—221no—
472C4—881no—
473C4—881no—
474C4—881no—
475C4#1062307911yescharacteristic
476C4D11×#13511yescharacteristic
477C2—161no—
478C2—441no—
479C2—1761no—
480C2#1307919211yescharacteristic
481C2#1308175811yescharacteristic
482C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13079262C2
hypercenterC4×SD32D11
hypocenterC11#33743
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #13079271C2semidirect
3. #13070894C2semidirect
4. #13070870C2semidirect
5. #13070860C2semidirect
6. #13070856C2semidirect
7. #13070732C2semidirect
8. #13070728C2semidirect
9. #13070713C2semidirect
10. #13070709C2semidirect
11. #13070480C2semidirect
12. #13070478C2semidirect
13. C4×#66864C2semidirect
14. #13070211C2semidirect
15. C4×C11×SD32C2semidirect
190. C4×SD32D11semidirect
417. C11#33743semidirect

Maximal subgroups

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

subgroupindex
#130792712
#130792622
#130708942
#130708702
#130708602
#130708562
#130707322
#130707282
#130707132
#130707092
#130704802
#130704782
C4×#668642
#130702112
C4×C11×SD322
#3374311