Finite Group Databasebeta

← #14798872

Subgroups — #14798872

Order 2816.

642 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#13078336C211yesmaximal, characteristic
2#13077418C211yesmaximal, characteristic, complemented
3#13070072C212yesmaximal, complemented
4#13069920C212yesmaximal, complemented
5#13069514C211yesmaximal, characteristic, complemented
6#13069369C211yesmaximal, characteristic, complemented
7#13069120C212yesmaximal, complemented
8#13068740C211yesmaximal, characteristic, complemented
9#13068719C212yesmaximal, complemented
10#13068662C211yesmaximal, characteristic, complemented
11C11×#1765C211yesmaximal, characteristic, complemented
12C2×C11×#131C2211yescharacteristic
13#10623353C2212yes—
14C2×#66957C2211yescharacteristic
15C4×#4339C2212yes—
16C2×C11×#104C2211yescharacteristic
17C11×#416C2211yescharacteristic
18C11×#405C2211yescharacteristic
19C2×C11×#97C2211yescharacteristic
20#10622853C2212yes—
21#10622756—21no—
22#10622755—21no—
23#10622754—22no—
24#10622752C2212yes—
25#10622745C2212yes—
26#10622726C2212yes—
27C2×#66883C2211yescharacteristic
28#10622719C2211yescharacteristic
29#10622719C2211yescharacteristic
30#10622715C2212yes—
31#10622619C2212yes—
32#10622329—21no—
33#10622324—21no—
34#10622323—22no—
35C11×#341C2211yescharacteristic
36C11×#339C2211yescharacteristic
37#10622195C2212yes—
38#10622194C2212yes—
39#10622169C2212yes—
40#10622161C2212yes—
41C2×C11×#41C2311yescharacteristic
42C2×#4339C2312yes—
43C11×#131—21no—
44C11×#131—21no—
45C11×#131—21no—
46C11×#131—21no—
47C2×C11×M16—21no—
48C2×C11×M16C2311yescharacteristic
49C2×C11×M16C2311yescharacteristic
50C22×C8×C11—21no—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×#117C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55#67004—22no—
56#67003—42no—
57#67002—22no—
58#66995—22no—
59#66985—22no—
60C4×C22⋊D11—42no—
61#66979C2312yes—
62#66979C2312yes—
63C2×#4318C2312yes—
64C2×Dic44D411yescharacteristic
65#66957—21no—
66#66957—21no—
67#66957—21no—
68#66957—21no—
69C2×D88D411yescharacteristic
70C2×#4314D412yes—
71C4×D44—22no—
72#66925—22no—
73C42×D11—22no—
74C4×Dic22—22no—
75C11×#104—22no—
76C11×#103—21no—
77C11×#102—21no—
78C11×#97—21no—
79C11×#97—21no—
80C11×#97—21no—
81C4×C8×C11—21no—
82#66898—42no—
83#66889—42no—
84#66888—22no—
85#66887—22no—
86#66885—22no—
87#66883—21no—
88#66883—21no—
89#66882—21no—
90#66882—21no—
91#66881—21no—
92#66881—21no—
93#66880—22no—
94Dic11⋊C8—42no—
95#66870—42no—
96#24986—111nomaximal, Sylow
97C11×#41—21no—
98C11×#41—21no—
99C11×#41—21no—
100C11×#41—21no—
101C2×Q8×C11#4111yescharacteristic
102C2×D4×C11—21no—
103C2×D4×C11#4111yescharacteristic
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—22no—
108#4339—22no—
109#4339—22no—
110#4339—22no—
111#4339—22no—
112C2×D44C2×D412yes—
113C2×C4×D11—22no—
114C2×C4×D11—42no—
115C2×Dic22C2×D412yes—
116C11×M16—21no—
117C11×M16—21no—
118C11×M16—21no—
119C11×M16—21no—
120C11×M16—41no—
121C11×M16—41no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11#4111yescharacteristic
132C2×C8×C11#4111yescharacteristic
133C2×C8×C11#4111yescharacteristic
134C2×C8×C11#4111yescharacteristic
135C11×C4⋊C4—21no—
136C11×C22⋊C4—21no—
137C42×C11—21no—
138C42×C11—21no—
139C42×C11#4112yes—
140C22⋊Dic11—22no—
141C22⋊Dic11—22no—
142#4326—42no—
143#4325—42no—
144#4324—42no—
145#4323—42no—
146(C2×D11)⋊C4—42no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149Dic11⋊C4—42no—
150C4×Dic11—22no—
151C4×Dic11—22no—
152C4×Dic11—42no—
153#4318—22no—
154#4318—22no—
155C2×C11⋊C8—22no—
156Dic44—21no—
157Dic44—21no—
158D88—21no—
159D88—21no—
160#4314—22no—
161#4314—22no—
162#3067—111no—
163#2943—111no—
164#2080—112no—
165#2053—112no—
166#1976—111no—
167#1946—111no—
168#1906—112no—
169#1833—111no—
170#1827—112no—
171#1812—111no—
172#1765D1111yescharacteristic, complemented
173C23×C11—21no—
174C23×C11H(5,𝔽2)11yescharacteristic
175C22×D11—22no—
176Q8×C11—21no—
177Q8×C11—21no—
178D4×C11—21no—
179D4×C11—21no—
180D4×C11—41no—
181D4×C11—41no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—81no—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C22⋊D11—42no—
195C22⋊D11—42no—
196C2×Dic11—22no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199D44—22no—
200D44—22no—
201C4×D11—42no—
202C4×D11—42no—
203C4×D11—84no—
204Dic22—22no—
205Dic22—22no—
206C8×C11—41no—
207C8×C11—41no—
208C8×C11—41no—
209C8×C11#12311yescharacteristic
210C8×C11#12311yescharacteristic
211C8×C11#12311yescharacteristic
212C8×C11#12311yescharacteristic
213C11⋊C8—42no—
214#575—112no—
215C2×#135—111no—
216C2×#131C2×D1111yescharacteristic
217C4×#41—112no—
218#473—221no—
219#472—221no—
220#471—222no—
221#442—221no—
222#441—221no—
223#440—222no—
224C2×#108—111no—
225#427—111no—
226#427—111no—
227#424—112no—
228#421—112no—
229C2×#104C2×D1111yescharacteristic
230#416—112no—
231#416C2×D1111yescharacteristic
232#413—112no—
233#410—112no—
234#410—112no—
235#405C2×D1111yescharacteristic
236C2×#97C2×D1111yescharacteristic
237#344—112no—
238#341C2×D1111yescharacteristic
239#339—112no—
240#339C2×D1111yescharacteristic
241H(3,ℤ/4)—112no—
242H(3,ℤ/4)—112no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—81no—
246C22×C11#54011yescharacteristic
247C22×C11#54611yescharacteristic
248C22×C11#55311yescharacteristic
249C2×D11—42no—
250C2×D11—82no—
251C4×C11—42no—
252C4×C11—41no—
253C4×C11—81no—
254C4×C11C2×#12311yescharacteristic
255C4×C11#52911yescharacteristic
256C4×C11#54611yescharacteristic
257C4×C11#55511yescharacteristic
258Dic11—42no—
259Dic11—82no—
260Dic11—82no—
261C2×#41—112no—
262C2×#41C22×D1111yescharacteristic
263#137—222no—
264#137—222no—
265AGL(1,ℤ/8)—222no—
266AGL(1,ℤ/8)—222no—
267#135—221no—
268#135—221no—
269#135—221no—
270#135—221no—
271#135—442no—
272C2×Q16—111no—
273C2×SD16—112no—
274C2×D8—111no—
275#131—21no—
276#131—21no—
277#131—21no—
278#131—21no—
279C2×M16—21no—
280C2×M16—112no—
281C2×M16C22×D1111yescharacteristic
282C2×M16C22×D1111yescharacteristic
283C22×C8—21no—
284C22×C8C22×D1111yescharacteristic
285C22×C8C22×D1111yescharacteristic
286C4×Q8—222no—
287C4×D4—222no—
288C4×D4—442no—
289#117—112no—
290#117—112no—
291#117—222no—
292#117C22×D1111yescharacteristic
293C2×C42—222no—
294C2×C42C22×D1111yescharacteristic
295#108—221no—
296#108—221no—
297#107—221no—
298#107—221no—
299#106—221no—
300#106—221no—
301C4⋊C8—442no—
302#104—22no—
303#104—442no—
304#103—21no—
305#103—222no—
306#102—21no—
307#102—222no—
308#101—222no—
309#100—222no—
310#99—442no—
311#99—442no—
312#97—21no—
313#97—21no—
314#97—21no—
315C4×C8—21no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—21no—
319C2×C11—81no—
320C2×C11#242011yescharacteristic
321D11—82no—
322#41—21no—
323#41—21no—
324#41—21no—
325#41—21no—
326#41—222no—
327#41—222no—
328#41—222no—
329#41—222no—
330C2×Q8—112no—
331C2×Q8#433911yescharacteristic
332C2×D4—21no—
333C2×D4—112no—
334C2×D4—222no—
335C2×D4#433911yescharacteristic
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—222no—
339C22×C4—442no—
340C22×C4C23×D1111yescharacteristic
341Q16—221no—
342Q16—221no—
343Q16—442no—
344SD16—222no—
345SD16—222no—
346SD16—442no—
347SD16—442no—
348D8—221no—
349D8—221no—
350D8—442no—
351M16—21no—
352M16—21no—
353M16—21no—
354M16—21no—
355M16—41no—
356M16—41no—
357M16—222no—
358M16—222no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—222no—
367C2×C8#433911yescharacteristic
368C2×C8#433911yescharacteristic
369C2×C8D4×D1111yescharacteristic
370C2×C8D4×D1111yescharacteristic
371C2×C8#434111yescharacteristic
372C2×C8#434111yescharacteristic
373C4⋊C4—21no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—442no—
377C22⋊C4—21no—
378C22⋊C4—222no—
379C22⋊C4—222no—
380C22⋊C4—442no—
381C42—21no—
382C42—21no—
383C42—222no—
384C42—222no—
385C42—442no—
386C42#433912yes—
387C11#2498611yescharacteristic, complemented, Sylow
388C23—21no—
389C23—222no—
390C23#6704211yescharacteristic
391Q8—21no—
392Q8—21no—
393Q8—222no—
394Q8—222no—
395D4—21no—
396D4—21no—
397D4—41no—
398D4—41no—
399D4—222no—
400D4—222no—
401D4—442no—
402D4—442no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—81no—
409C2×C4—222no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—884no—
415C2×C4C2×#433911yescharacteristic
416C2×C4C2×#433911yescharacteristic
417C2×C4C2×#433911yescharacteristic
418C2×C4C2×D4×D1111yescharacteristic
419C2×C4C2×#434111yescharacteristic
420C2×C4#6704211yescharacteristic
421C8—41no—
422C8—41no—
423C8—41no—
424C8—442no—
425C8#6693611yescharacteristic
426C8#6693611yescharacteristic
427C8#6693611yescharacteristic
428C8#6693611yescharacteristic
429C22—41no—
430C22—41no—
431C22—81no—
432C22—442no—
433C22—882no—
434C22#1062306611yescharacteristic
435C22#1062308111yescharacteristic
436C22#1062309611yescharacteristic
437C4—42no—
438C4—41no—
439C4—81no—
440C4—442no—
441C4—882no—
442C4—882no—
443C4#1062301011yescharacteristic
444C4C2×#6693611yescharacteristic
445C4#1062308111yescharacteristic
446C4#1062309411yescharacteristic
447C2—21no—
448C2—21no—
449C2—21no—
450C2—81no—
451C2—882no—
452C2#1307210811yescharacteristic
subgroupG/H
centerC4#10623094
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1765C2
socleC2×C11#2420
prime radical#13078336C2
hypercenter#1765D11
hypocenterC11#24986
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. #13077418C2semidirect
3. #13070072C2semidirect
4. #13069920C2semidirect
5. #13069514C2semidirect
6. #13069369C2semidirect
7. #13069120C2semidirect
8. #13068740C2semidirect
9. #13068719C2semidirect
10. #13068662C2semidirect
11. C11×#1765C2semidirect
172. #1765D11semidirect
387. C11#24986semidirect

Maximal subgroups

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

subgroupindex
#130783362
#130774182
#130700722
#130699202
#130695142
#130693692
#130691202
#130687402
#130687192
#130686622
C11×#17652
#2498611