Finite Group Databasebeta

← #14908976

Subgroups — #14908976

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079255C211yesmaximal, characteristic, complemented
2#13077493C211yesmaximal, characteristic, complemented
3#13070814C211yesmaximal, characteristic, complemented
4#13070802C211yesmaximal, characteristic, complemented
5#13070764C211yesmaximal, characteristic, complemented
6#13070759C211yesmaximal, characteristic, complemented
7#13070679C211yesmaximal, characteristic, complemented
8#13070672C211yesmaximal, characteristic, complemented
9#13070558C211yesmaximal, characteristic, complemented
10#13070541C211yesmaximal, characteristic
11#13070493C211yesmaximal, characteristic, complemented
12#13070488C211yesmaximal, characteristic, complemented
13C4×#66864C211yesmaximal, characteristic, complemented
14C4×#66864C211yesmaximal, characteristic, complemented
15C11×#2164C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17#10623065—21no—
18#10623054—21no—
19C11×#405C2211yescharacteristic
20#10622747—21no—
21#10622746—21no—
22#10622729C2211yescharacteristic
23#10622728C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×Dic88C2211yescharacteristic
26C2×#66864C2211yescharacteristic
27C2×#66864C2211yescharacteristic
28C2×D176C2211yescharacteristic
29#10622327—21no—
30#10622323—21no—
31#10622323—21no—
32#10622323—21no—
33C4×Dic44C2211yescharacteristic
34C4×Dic44C2211yescharacteristic
35C4×Dic44C2211yescharacteristic
36#10622309C2211yescharacteristic
37C4×D88C2211yescharacteristic
38C4×D88C2211yescharacteristic
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#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622143C2211yescharacteristic
53#10622143C2211yescharacteristic
54#10622143C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×#4339—21no—
60C2×C11×M16D411yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#117D411yescharacteristic
63#66983—21no—
64C2×C4⋊Dic11—21no—
65#66977—21no—
66C2×Dic44C2311yescharacteristic
67C2×Dic44C2311yescharacteristic
68#66957—22no—
69#66957—22no—
70C2×D88C2311yescharacteristic
71C2×D88C2311yescharacteristic
72C2×#4314—21no—
73C2×#4314—21no—
74#66951—41no—
75#66949—41no—
76#66945—41no—
77C4⋊C4×D11—41no—
78#66938—41no—
79#66936—41no—
80(C22⋊D11)⋊C4—41no—
81(C22⋊D11)⋊C4—41no—
82#66928—21no—
83C4×D44—21no—
84C4×D44—21no—
85C4×D44—21no—
86#66922—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#66885—21no—
101#66885—21no—
102#66882—21no—
103#66882—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109#66880—21no—
110#66880—21no—
111#66880—21no—
112Dic88—22no—
113#66864—22no—
114#66864—22no—
115D176—22no—
116#33685—111nomaximal, Sylow
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C22×Dic11—41no—
121#4339—24no—
122#4339—42no—
123C2×D44—21no—
124C2×D44—21no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—41no—
132C11×M16—41no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2411yescharacteristic
139C11×C4⋊C4D811yescharacteristic
140C11×C4⋊C4D811yescharacteristic
141C11×C22⋊C4D811yescharacteristic
142C11×C22⋊C4D811yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C22⋊Dic11—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165Dic44—21no—
166Dic44—21no—
167Dic44—21no—
168Dic44#4112yes—
169D88—21no—
170D88—21no—
171D88—21no—
172D88#4112yes—
173#4314—24no—
174#4314—42no—
175C11×C16—21no—
176C11×C16—21no—
177C11×C16—21no—
178C11×C16—21no—
179#3175—111no—
180#2951—111no—
181#2235—111no—
182#2233—111no—
183#2226—111no—
184#2225—111no—
185#2211—111no—
186#2210—111no—
187#2189—111no—
188#2186—111no—
189#2177—111no—
190#2176—111no—
191C4×SD32—111no—
192C4×SD32—111no—
193#2164D1111yescharacteristic, complemented
194C23×C11C2×D811yescharacteristic
195C22×D11—41no—
196C22×D11—41no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C22⋊D11—44no—
206C22⋊D11—161no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—161no—
214D44—22no—
215D44—41no—
216D44—41no—
217D44—41no—
218C4×D11—44no—
219C4×D11—161no—
220C4×D11—161no—
221C4×D11—161no—
222Dic22—22no—
223Dic22—41no—
224Dic22—41no—
225Dic22—41no—
226Dic22—161no—
227C8×C11—21no—
228C8×C11—21no—
229C8×C11—21no—
230C8×C11C2×#4111yescharacteristic
231C8×C11C2×#4111yescharacteristic
232C2×#135—111no—
233#542—221no—
234#520—221no—
235C2×Q32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×D16—111no—
239#500—111no—
240#495—111no—
241#489—221no—
242#468—221no—
243#467—111no—
244#466—111no—
245#440—221no—
246#440—221no—
247#440—221no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×Q16—111no—
251C4×D8—111no—
252C4×D8—111no—
253C4×D8—111no—
254C2×#107—111no—
255#417—221no—
256#405C2×D1111yescharacteristic
257#367—111no—
258#367—111no—
259#367—111no—
260#367—111no—
261C4⋊C16C2×D1111yescharacteristic
262C4⋊C16C2×D1111yescharacteristic
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271C22⋊C16C2×D1111yescharacteristic
272C22⋊C16C2×D1111yescharacteristic
273#346C2×D1111yescharacteristic
274C4×C16C2×D1111yescharacteristic
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11C22×D811yescharacteristic
279C2×D11—42no—
280C2×D11—81no—
281C2×D11—81no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11#52511yescharacteristic
291C4×C11#57511yescharacteristic
292Dic11—42no—
293Dic11—81no—
294Dic11—81no—
295Dic11—81no—
296Dic11—81no—
297Dic11—81no—
298C2×#41—221no—
299#135—222no—
300#135—222no—
301C2×Q16—111no—
302C2×Q16—111no—
303C2×SD16—221no—
304C2×SD16—221no—
305C2×D8—111no—
306C2×D8—111no—
307C2×M16D4411yescharacteristic
308C22×C8C22×D1111yescharacteristic
309C4⋊Q8—221no—
310#126—441no—
311#124—221no—
312#124—441no—
313#123—441no—
314C22⋊Q8—221no—
315C22⋊Q8—441no—
316#121—221no—
317C4×Q8—221no—
318C4×Q8—221no—
319C4×Q8—221no—
320C4×D4—221no—
321C4×D4—221no—
322C4×D4—221no—
323C4×D4—441no—
324C4×D4—441no—
325#117—441no—
326#117D4411yescharacteristic
327C2×C4⋊C4—221no—
328C2×C4⋊C4—441no—
329Q32—222no—
330SD32—222no—
331SD32—222no—
332D16—222no—
333C2×C16C22×D1111yescharacteristic
334C2×C16C22×D1111yescharacteristic
335C2×C16C22×D1111yescharacteristic
336C2×C16C22×D1111yescharacteristic
337#107—111no—
338#107—111no—
339#107—111no—
340#107—111no—
341#107—221no—
342#107—221no—
343#103—221no—
344#103—221no—
345#103—221no—
346#103—221no—
347#102—221no—
348#102—221no—
349#102—221no—
350#102—221no—
351#97D4411yescharacteristic
352#97D4411yescharacteristic
353C4×C8C22×D1111yescharacteristic
354C4×C8C22×D1111yescharacteristic
355C2×C11—41no—
356C2×C11#310011yescharacteristic
357C2×C11#341611yescharacteristic
358C2×C11#341611yescharacteristic
359D11—82no—
360D11—161no—
361#41—224no—
362#41—442no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×Q8—441no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—441no—
369C2×D4—441no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4C2×D4411yescharacteristic
376Q16—112no—
377Q16—221no—
378Q16—221no—
379Q16—221no—
380SD16—224no—
381SD16—442no—
382D8—112no—
383D8—221no—
384D8—221no—
385D8—221no—
386M16—41no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8C2×D4411yescharacteristic
390C2×C8C2×D4411yescharacteristic
391C2×C8C2×D4411yescharacteristic
392C2×C8C23×D1111yescharacteristic
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4D8811yescharacteristic
404C4⋊C4D8811yescharacteristic
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4D8811yescharacteristic
413C22⋊C4D8811yescharacteristic
414C42—441no—
415C42—441no—
416C42—441no—
417C42C2×D4411yescharacteristic
418C42C2×D4411yescharacteristic
419C16—21no—
420C16—21no—
421C16—21no—
422C16—21no—
423C11#3368511yescharacteristic, complemented, Sylow
424C23—441no—
425C23—441no—
426C23C2×D8811yescharacteristic
427Q8—222no—
428Q8—441no—
429Q8—441no—
430Q8—441no—
431Q8—1761no—
432D4—222no—
433D4—444no—
434D4—441no—
435D4—441no—
436D4—441no—
437D4—1761no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—444no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—1761no—
448C2×C4—1761no—
449C2×C4—1761no—
450C2×C4—1761no—
451C2×C4C2×D8811yescharacteristic
452C2×C4C2×D8811yescharacteristic
453C2×C4C2×D8811yescharacteristic
454C2×C4C2×D8811yescharacteristic
455C2×C4C2×D8811yescharacteristic
456C2×C4C22×D4411yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8#41×D1111yescharacteristic
461C8#41×D1111yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—442no—
466C22—881no—
467C22—881no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22C22×D8811yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—442no—
478C4—881no—
479C4—881no—
480C4—881no—
481C4—881no—
482C4—881no—
483C4#1062305511yescharacteristic
484C4#1062327911yescharacteristic
485C2—41no—
486C2—882no—
487C2—1761no—
488C2#1307861711yescharacteristic
489C2#1308176411yescharacteristic
490C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2164C2
socleC22×C11C22×D8
prime radical#13070541C2
hypercenter#2164D11
hypocenterC11#33685
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
1. #13079255C2semidirect
2. #13077493C2semidirect
3. #13070814C2semidirect
4. #13070802C2semidirect
5. #13070764C2semidirect
6. #13070759C2semidirect
7. #13070679C2semidirect
8. #13070672C2semidirect
9. #13070558C2semidirect
11. #13070493C2semidirect
12. #13070488C2semidirect
13. C4×#66864C2semidirect
14. C4×#66864C2semidirect
15. C11×#2164C2semidirect
193. #2164D11semidirect
423. C11#33685semidirect

Maximal subgroups

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

subgroupindex
#130792552
#130774932
#130708142
#130708022
#130707642
#130707592
#130706792
#130706722
#130705582
#130705412
#130704932
#130704882
C4×#668642
C11×#21642
#3368511