Finite Group Databasebeta

← #14908928

Subgroups — #14908928

Order 2816.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079255C211yesmaximal, characteristic
2#13077485C211yesmaximal, characteristic, complemented
3#13070825C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic
5#13070769C211yesmaximal, characteristic, complemented
6#13070759C211yesmaximal, characteristic, complemented
7#13070679C211yesmaximal, characteristic, complemented
8#13070679C211yesmaximal, characteristic, complemented
9#13070552C211yesmaximal, characteristic, complemented
10#13070535C211yesmaximal, characteristic
11#13070488C211yesmaximal, characteristic, complemented
12#13070482C211yesmaximal, characteristic, complemented
13C4×Dic88C211yesmaximal, characteristic, complemented
14C4×#66864C211yesmaximal, characteristic, complemented
15C11×#2164C211yesmaximal, characteristic, complemented
16C22×Dic44C2211yescharacteristic
17#10623065—21no—
18#10623047—21no—
19C11×#405C2211yescharacteristic
20#10622747—21no—
21#10622733—21no—
22#10622729C2211yescharacteristic
23#10622728C2211yescharacteristic
24#10622719C2211yescharacteristic
25C2×Dic88C2211yescharacteristic
26C2×Dic88C2211yescharacteristic
27C2×#66864C2211yescharacteristic
28C2×#66864C2211yescharacteristic
29#10622329—21no—
30#10622329—21no—
31#10622327—21no—
32#10622323—21no—
33C4×Dic44C2211yescharacteristic
34C4×Dic44C2211yescharacteristic
35C4×Dic44C2211yescharacteristic
36C4×Dic44C2211yescharacteristic
37C4×Dic44C2211yescharacteristic
38#10622309C2211yescharacteristic
39C4×D88C2211yescharacteristic
40#10622295C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C11×#346C2211yescharacteristic
46C4×C11×C16C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C22×Dic22—21no—
60C2×C11×M16D411yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#117D411yescharacteristic
63#66983—21no—
64#66979—21no—
65#66977—21no—
66C2×Dic44—21no—
67C2×Dic44—22no—
68C2×Dic44—22no—
69C2×Dic44C2311yescharacteristic
70C2×Dic44C2311yescharacteristic
71C2×Dic44C2311yescharacteristic
72C2×D88C2311yescharacteristic
73C2×#4314—21no—
74#66951—41no—
75#66949—41no—
76#66940—41no—
77#66940—41no—
78#66938—41no—
79#66936—41no—
80#66930—41no—
81#66930—41no—
82#66928—21no—
83C4×D44—21no—
84#66922—21no—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C4×Dic22—21no—
88C4×Dic22—21no—
89C4×Dic22—21no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#97D411yescharacteristic
95C11×#97D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97C4×C8×C11C2311yescharacteristic
98#66885—21no—
99#66885—21no—
100#66882—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106#66880—21no—
107#66880—21no—
108#66880—21no—
109#66880—21no—
110#66880—21no—
111#66880—21no—
112Dic88—22no—
113Dic88—22no—
114#66864—22no—
115#66864—22no—
116#33681—111nomaximal, Sylow
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C22×Dic11—41no—
120C2×D44—21no—
121C2×C4×D11—41no—
122C2×Dic22—24no—
123C2×Dic22—21no—
124C2×Dic22—21no—
125C2×Dic22—21no—
126C2×Dic22—42no—
127C2×Dic22—41no—
128C2×Dic22—41no—
129C11×M16—41no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2411yescharacteristic
136C11×C4⋊C4D811yescharacteristic
137C11×C4⋊C4D811yescharacteristic
138C11×C22⋊C4D811yescharacteristic
139C11×C22⋊C4D811yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C22⋊Dic11—41no—
143C22⋊Dic11—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165Dic44—24no—
166Dic44—21no—
167Dic44—21no—
168Dic44—21no—
169Dic44—21no—
170Dic44#4112yes—
171Dic44#4112yes—
172D88—21no—
173D88—21no—
174#4314—42no—
175C11×C16—21no—
176C11×C16—21no—
177C11×C16—21no—
178C11×C16—21no—
179#3175—111no—
180#2950—111no—
181#2237—111no—
182#2234—111no—
183#2227—111no—
184#2225—111no—
185#2211—111no—
186#2211—111no—
187#2188—111no—
188#2185—111no—
189#2176—111no—
190#2175—111no—
191C4×Q32—111no—
192C4×SD32—111no—
193#2164D1111yescharacteristic, complemented
194C23×C11C2×D811yescharacteristic
195C22×D11—41no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C22⋊D11—161no—
205C2×Dic11—44no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213D44—41no—
214D44—41no—
215C4×D11—161no—
216Dic22—22no—
217Dic22—22no—
218Dic22—44no—
219Dic22—41no—
220Dic22—41no—
221Dic22—41no—
222Dic22—41no—
223Dic22—161no—
224C8×C11—21no—
225C8×C11—21no—
226C8×C11—21no—
227C8×C11C2×#4111yescharacteristic
228C8×C11C2×#4111yescharacteristic
229C22×Q16—111no—
230#542—221no—
231#519—221no—
232C2×Q32—111no—
233C2×Q32—111no—
234C2×SD32—111no—
235C2×SD32—111no—
236#500—111no—
237#495—111no—
238#489—221no—
239#468—221no—
240#467—111no—
241#466—111no—
242#441—221no—
243#441—221no—
244#440—221no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×D8—111no—
251#427—111no—
252#419—221no—
253#405C2×D1111yescharacteristic
254#367—111no—
255#367—111no—
256#366—111no—
257#366—111no—
258C4⋊C16C2×D1111yescharacteristic
259C4⋊C16C2×D1111yescharacteristic
260#358—111no—
261#358—111no—
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#357—111no—
267#357—111no—
268C22⋊C16C2×D1111yescharacteristic
269C22⋊C16C2×D1111yescharacteristic
270#346C2×D1111yescharacteristic
271C4×C16C2×D1111yescharacteristic
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11C22×D811yescharacteristic
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11#52511yescharacteristic
285C4×C11#57511yescharacteristic
286Dic11—42no—
287Dic11—42no—
288Dic11—81no—
289Dic11—81no—
290Dic11—81no—
291Dic11—81no—
292Dic11—81no—
293C22×Q8—221no—
294C2×Q16—111no—
295C2×Q16—111no—
296C2×Q16—111no—
297C2×Q16—222no—
298C2×Q16—222no—
299C2×Q16—221no—
300C2×SD16—221no—
301C2×D8—111no—
302C2×M16D4411yescharacteristic
303C22×C8C22×D1111yescharacteristic
304C4⋊Q8—221no—
305#126—441no—
306#124—221no—
307#124—441no—
308#123—441no—
309C22⋊Q8—221no—
310C22⋊Q8—441no—
311#121—221no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×Q8—441no—
318C4×Q8—441no—
319C4×D4—221no—
320#117—221no—
321#117—441no—
322#117—441no—
323#117D4411yescharacteristic
324Q32—222no—
325Q32—222no—
326SD32—222no—
327SD32—222no—
328C2×C16C22×D1111yescharacteristic
329C2×C16C22×D1111yescharacteristic
330C2×C16C22×D1111yescharacteristic
331C2×C16C22×D1111yescharacteristic
332#107—111no—
333#107—111no—
334#107—111no—
335#107—111no—
336#107—221no—
337#106—221no—
338#103—221no—
339#103—221no—
340#103—221no—
341#103—221no—
342#103—221no—
343#103—221no—
344#102—221no—
345#102—221no—
346#97D4411yescharacteristic
347#97D4411yescharacteristic
348C4×C8C22×D1111yescharacteristic
349C4×C8C22×D1111yescharacteristic
350C2×C11—41no—
351C2×C11#310011yescharacteristic
352C2×C11#341611yescharacteristic
353C2×C11#341711yescharacteristic
354D11—161no—
355C2×Q8—224no—
356C2×Q8—221no—
357C2×Q8—221no—
358C2×Q8—221no—
359C2×Q8—442no—
360C2×Q8—441no—
361C2×Q8—441no—
362C2×D4—221no—
363C2×D4—441no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4C2×D4411yescharacteristic
367Q16—112no—
368Q16—112no—
369Q16—224no—
370Q16—221no—
371Q16—221no—
372Q16—221no—
373Q16—221no—
374SD16—442no—
375D8—221no—
376D8—221no—
377M16—41no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8C2×D4411yescharacteristic
381C2×C8C2×D4411yescharacteristic
382C2×C8C2×D4411yescharacteristic
383C2×C8C23×D1111yescharacteristic
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4D8811yescharacteristic
396C4⋊C4D8811yescharacteristic
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4D8811yescharacteristic
404C22⋊C4D8811yescharacteristic
405C42—441no—
406C42—441no—
407C42—441no—
408C42—441no—
409C42—441no—
410C42—441no—
411C42C2×D4411yescharacteristic
412C42C2×D4411yescharacteristic
413C16—21no—
414C16—21no—
415C16—21no—
416C16—21no—
417C11#3368111yescharacteristic, complemented, Sylow
418C23—441no—
419C23C2×D8811yescharacteristic
420Q8—222no—
421Q8—222no—
422Q8—444no—
423Q8—441no—
424Q8—441no—
425Q8—441no—
426Q8—441no—
427Q8—1761no—
428D4—441no—
429D4—441no—
430D4—1761no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—444no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—1761no—
442C2×C4C2×D8811yescharacteristic
443C2×C4C2×D8811yescharacteristic
444C2×C4C2×D8811yescharacteristic
445C2×C4C2×D8811yescharacteristic
446C2×C4C2×D8811yescharacteristic
447C2×C4C22×D4411yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8#41×D1111yescharacteristic
452C8#41×D1111yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—881no—
457C22—881no—
458C22—881no—
459C22C22×D8811yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—442no—
466C4—442no—
467C4—881no—
468C4—881no—
469C4—881no—
470C4—881no—
471C4—881no—
472C4#1062305511yescharacteristic
473C4#1062327911yescharacteristic
474C2—41no—
475C2—1761no—
476C2#1307861711yescharacteristic
477C2#1308176411yescharacteristic
478C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2164C2
socleC22×C11C22×D8
prime radical#10622728C22
hypercenter#2164D11
hypocenterC11#33681
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2164

Complements

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

NH ≅ G/Ntype
2. #13077485C2semidirect
3. #13070825C2semidirect
5. #13070769C2semidirect
6. #13070759C2semidirect
7. #13070679C2semidirect
8. #13070679C2semidirect
9. #13070552C2semidirect
11. #13070488C2semidirect
12. #13070482C2semidirect
13. C4×Dic88C2semidirect
14. C4×#66864C2semidirect
15. C11×#2164C2semidirect
193. #2164D11semidirect
417. C11#33681semidirect

Maximal subgroups

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

subgroupindex
#130792552
#130774852
#130708252
#130708082
#130707692
#130707592
#130706792
#130705522
#130705352
#130704882
#130704822
C4×Dic882
C4×#668642
C11×#21642
#3368111