Finite Group Databasebeta

← #14911300

Subgroups — #14911300

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081039C211yesmaximal, characteristic
2#13080985C211yesmaximal, characteristic, complemented
3#13070902C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070825C211yesmaximal, characteristic, complemented
6#13070808C211yesmaximal, characteristic, complemented
7#13070802C211yesmaximal, characteristic, complemented
8#13070774C211yesmaximal, characteristic, complemented
9#13070759C211yesmaximal, characteristic, complemented
10#13070729C211yesmaximal, characteristic, complemented
11#13070712C211yesmaximal, characteristic, complemented
12#13070482C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14#13070400C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16#10623094—21no—
17#10623072—21no—
18C2×C11×M32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622729C2211yescharacteristic
22#10622729C2211yescharacteristic
23#10622728C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622719C2211yescharacteristic
26#10622719C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66864C2211yescharacteristic
30#10622455—21no—
31#10622442—21no—
32#10622350—21no—
33#10622350—21no—
34#10622336—21no—
35#10622334—21no—
36C4×Dic44C2211yescharacteristic
37C4×D88C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×C22⋊C16C2211yescharacteristic
42C11×C22⋊C16C2211yescharacteristic
43C11×#346C2211yescharacteristic
44#10622147C2211yescharacteristic
45#10622147C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622142C2211yescharacteristic
54#10622142C2211yescharacteristic
55#10622142C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C4×D4×C11D411yescharacteristic
62#66991—41no—
63#66988—41no—
64#66983—21no—
65#66983—21no—
66#66979—21no—
67#66979—21no—
68#66979—21no—
69C2×C4⋊Dic11—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73C2×D88C2311yescharacteristic
74#66945—41no—
75#66942—41no—
76#66938—41no—
77#66938—41no—
78#66932—41no—
79#66930—41no—
80C4×D44—21no—
81#66923—21no—
82#66922—21no—
83C4×Dic22—21no—
84C11×M32—22no—
85C2×C11×C16—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×C22⋊C8D411yescharacteristic
92C11×C22⋊C8D411yescharacteristic
93C4×C8×C11C2311yescharacteristic
94#66885—21no—
95#66885—21no—
96#66885—21no—
97#66882—21no—
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106#66881—21no—
107#66881—21no—
108#66881—21no—
109#66880—21no—
110#66880—21no—
111#66880—21no—
112#66864—22no—
113#33915—111nomaximal, Sylow
114C2×D4×C11D811yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C22×Dic11—41no—
120C2×D44—21no—
121C2×C4×D11—41no—
122C2×Dic22—21no—
123C2×Dic22—41no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4D811yescharacteristic
133C11×C22⋊C4D811yescharacteristic
134C11×C22⋊C4D811yescharacteristic
135C42×C11C2×D411yescharacteristic
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161Dic44—21no—
162Dic44—21no—
163D88—21no—
164D88—21no—
165C11×C16—21no—
166C11×C16—21no—
167C11×C16—21no—
168C11×C16#4112yes—
169#3341—111no—
170#3336—111no—
171#2255—111no—
172#2237—111no—
173#2237—111no—
174#2234—111no—
175#2233—111no—
176#2228—111no—
177#2225—111no—
178#2220—111no—
179#2217—111no—
180#2175—111no—
181#2168D1111yescharacteristic, complemented
182#2159—111no—
183#2158—111no—
184C23×C11C2×D811yescharacteristic
185C23×C11C2×D811yescharacteristic
186C22×D11—41no—
187D4×C11—41no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C22⋊D11—161no—
198C22⋊D11—161no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—82no—
207D44—41no—
208D44—41no—
209C4×D11—82no—
210Dic22—41no—
211Dic22—41no—
212Dic22—161no—
213C8×C11—21no—
214C8×C11—21no—
215C8×C11—21no—
216C8×C11C2×#4111yescharacteristic
217C8×C112−1+411yescharacteristic
218#555—221no—
219#552—221no—
220C2×SD32—111no—
221C2×M32C2×D1111yescharacteristic
222C22×C16C2×D1111yescharacteristic
223#500—111no—
224#499—111no—
225#485—221no—
226#483—221no—
227#482—221no—
228#482—221no—
229#479—221no—
230#476—221no—
231#467—111no—
232#467—111no—
233#466—111no—
234#466—111no—
235C4×Q16—111no—
236C4×D8—111no—
237C8×D4C2×D1111yescharacteristic
238#427—111no—
239#427—111no—
240#427—111no—
241C2×#107—111no—
242#367—111no—
243#367—111no—
244#367—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251C4⋊C16C2×D1111yescharacteristic
252#358—111no—
253#358—111no—
254#358—111no—
255#357—111no—
256#357—111no—
257#357—111no—
258C22⋊C16C2×D1111yescharacteristic
259C22⋊C16C2×D1111yescharacteristic
260#346C2×D1111yescharacteristic
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11C22×D811yescharacteristic
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11#54711yescharacteristic
276C4×C11#57811yescharacteristic
277Dic11—81no—
278Dic11—81no—
279Dic11—81no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284C2×Q16—111no—
285C2×D8—111no—
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—221no—
289#126—441no—
290#125—221no—
291#125—441no—
292#124—441no—
293#124—441no—
294#123—441no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297#121—221no—
298#121—221no—
299#121—441no—
300C4×Q8—221no—
301C4×D4—221no—
302C4×D4D4411yescharacteristic
303#117—221no—
304#117—221no—
305#117—221no—
306#117—441no—
307#117—441no—
308C2×C4⋊C4—221no—
309SD32—222no—
310M32—22no—
311C2×C16—22no—
312C2×C16C22×D1111yescharacteristic
313C2×C16C22×D1111yescharacteristic
314C2×C16C22×D1111yescharacteristic
315C2×C16C22×D1111yescharacteristic
316#107—111no—
317#107—111no—
318#107—111no—
319#107—111no—
320#107—111no—
321#107—111no—
322#107—221no—
323#107—221no—
324#106—221no—
325#106—221no—
326#106—221no—
327#106—221no—
328C4⋊C8D4411yescharacteristic
329#103—221no—
330#103—221no—
331#103—221no—
332#102—221no—
333#102—221no—
334#102—221no—
335C22⋊C8D4411yescharacteristic
336C22⋊C8D4411yescharacteristic
337C4×C8C22×D1111yescharacteristic
338C2×C11—41no—
339C2×C11—41no—
340C2×C11#333411yescharacteristic
341C2×C11#341411yescharacteristic
342C2×C11#341611yescharacteristic
343D11—161no—
344C2×Q8—221no—
345C2×Q8—441no—
346C2×D4—221no—
347C2×D4—441no—
348C2×D4—441no—
349C2×D4D8811yescharacteristic
350C22×C4—441no—
351C22×C4—441no—
352C22×C4C2×D4411yescharacteristic
353C22×C4C2×D4411yescharacteristic
354Q16—221no—
355Q16—221no—
356D8—221no—
357D8—221no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8C2×D4411yescharacteristic
363C2×C8C2×D4411yescharacteristic
364C2×C8C2×D4411yescharacteristic
365C2×C8C23×D1111yescharacteristic
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4D8811yescharacteristic
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4D8811yescharacteristic
389C22⋊C4D8811yescharacteristic
390C42—441no—
391C42—441no—
392C42—441no—
393C42—441no—
394C42C2×D4411yescharacteristic
395C16—21no—
396C16—21no—
397C16—21no—
398C16#434112yes—
399C11#3391511yescharacteristic, complemented, Sylow
400C23—441no—
401C23C2×D8811yescharacteristic
402C23C2×D8811yescharacteristic
403Q8—441no—
404Q8—441no—
405Q8—1761no—
406D4—41no—
407D4—441no—
408D4—441no—
409D4—1761no—
410D4—1761no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—882no—
423C2×C4—882no—
424C2×C4C2×D8811yescharacteristic
425C2×C4C2×D8811yescharacteristic
426C2×C4C2×D8811yescharacteristic
427C2×C4C2×D8811yescharacteristic
428C2×C4C22×D4411yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8C2×#434111yescharacteristic
433C8#6704311yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—881no—
441C22—881no—
442C22—881no—
443C22C22×D8811yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—881no—
449C4—881no—
450C4—881no—
451C4—881no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4#1062308611yescharacteristic
456C4#1062328411yescharacteristic
457C2—41no—
458C2—41no—
459C2—1761no—
460C2#1308096411yescharacteristic
461C2#1308175211yescharacteristic
462C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
prime radical#13081039C2
hypercenter#2168D11
hypocenterC11#33915
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
2. #13080985C2semidirect
3. #13070902C2semidirect
4. #13070825C2semidirect
5. #13070825C2semidirect
6. #13070808C2semidirect
7. #13070802C2semidirect
8. #13070774C2semidirect
9. #13070759C2semidirect
10. #13070729C2semidirect
11. #13070712C2semidirect
12. #13070482C2semidirect
13. #13070404C2semidirect
14. #13070400C2semidirect
15. C11×#2168C2semidirect
181. #2168D11semidirect
399. C11#33915semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130809852
#130709022
#130708252
#130708082
#130708022
#130707742
#130707592
#130707292
#130707122
#130704822
#130704042
#130704002
C11×#21682
#3391511