Finite Group Databasebeta

← #14908852

Subgroups — #14908852

Order 2816.

548 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#13079197C211yesmaximal, characteristic, complemented
2#135×Dic11C211yesmaximal, characteristic
3#13070825C211yesmaximal, characteristic, complemented
4#13070821C211yesmaximal, characteristic, complemented
5#13070766C211yesmaximal, characteristic, complemented
6#13070761C211yesmaximal, characteristic, complemented
7#13070664C211yesmaximal, characteristic, complemented
8#13070659C211yesmaximal, characteristic, complemented
9#13070556C211yesmaximal, characteristic
10#13070487C211yesmaximal, characteristic, complemented
11#13070484C211yesmaximal, characteristic, complemented
12#13070481C211yesmaximal, characteristic, complemented
13#13070477C211yesmaximal, characteristic, complemented
14#13070416C211yesmaximal, characteristic, complemented
15C11×#2189C211yesmaximal, characteristic
16C2×C11×#135C2211yescharacteristic
17#41×Dic11—21no—
18#10623153—21no—
19C2×C11×Q32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C11×#467C2211yescharacteristic
22#10622846—21no—
23Q16×Dic11C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25Q16×Dic11C2211yescharacteristic
26#10622794C2211yescharacteristic
27C2×#66893C2211yescharacteristic
28SD16×Dic11—21no—
29SD16×Dic11—21no—
30D8×Dic11C2211yescharacteristic
31D8×Dic11C2211yescharacteristic
32C2×#66891C2211yescharacteristic
33#10622729C2211yescharacteristic
34#10622719C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622664—21no—
37#10622487C2211yescharacteristic
38#10622486C2211yescharacteristic
39#10622405—21no—
40#10622403—21no—
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622140C2211yescharacteristic
54#10622140C2211yescharacteristic
55Dic11⋊C16C2211yescharacteristic
56Dic11⋊C16C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×#41—21no—
60C11×#135—22no—
61C11×#135—22no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×Q16C2311yescharacteristic
64C2×C11×SD16—21no—
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C22⋊Q8—21no—
68Q8×Dic11—21no—
69Q8×Dic11—21no—
70Q8×Dic11—21no—
71#66997—21no—
72C2×#4326—21no—
73D4×Dic11—21no—
74D4×Dic11—21no—
75D4×Dic11—41no—
76D4×Dic11—41no—
77#66979—21no—
78#66979—41no—
79#66977—21no—
80C2×C4×Dic11—41no—
81C2×C4×Dic11D411yescharacteristic
82C22×C11⋊C8D411yescharacteristic
83C2×Dic44C2311yescharacteristic
84#66942—41no—
85#66941—21no—
86#66940—21no—
87#66940—41no—
88#66931—41no—
89#66930—41no—
90C11×Q32—22no—
91C11×SD32—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#103—21no—
96#66899—21no—
97#66899—21no—
98#66899—21no—
99#66896—21no—
100#66896—21no—
101#66893—22no—
102#66891—22no—
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66881—21no—
107#66880—21no—
108C8×Dic11D411yescharacteristic
109C8×Dic11D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66874—21no—
115#66871—21no—
116#33676—111nomaximal, Sylow
117C11×#41—24no—
118C11×#41—42no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11D811yescharacteristic
128C22×Dic11D811yescharacteristic
129C2×Dic22—21no—
130C2×Dic22—41no—
131C11×Q16—21no—
132C11×Q16—21no—
133C11×Q16—21no—
134C11×Q16#4112yes—
135C11×SD16—24no—
136C11×D8—21no—
137C11×D8#4112yes—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C22⋊C4—41no—
145C22⋊Dic11—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149#4326—42no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—41no—
154C4⋊Dic11—41no—
155C4⋊Dic11—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11D811yescharacteristic
167C4×Dic11D811yescharacteristic
168C4×Dic11C2×D411yescharacteristic
169C4×Dic11C2×D411yescharacteristic
170C2×C11⋊C8—41no—
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173Dic44—21no—
174Dic44—21no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3170—111no—
180C4×#135—111no—
181#2237—111no—
182#2237—111no—
183#2227—111no—
184#2226—111no—
185#2209—111no—
186#2208—111no—
187#2189—111no—
188#2189D1111yescharacteristic
189#2176—111no—
190#2176—111no—
191#2175—111no—
192#2175—111no—
193#2163—111no—
194C23×C11—41no—
195C23×C11C2×D811yescharacteristic
196Q8×C11—22no—
197Q8×C11—41no—
198Q8×C11—41no—
199Q8×C11—41no—
200D4×C11—22no—
201D4×C11—44no—
202D4×C11—41no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—44no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—82no—
218C2×Dic11—82no—
219C2×Dic11C2×D811yescharacteristic
220C2×Dic11C2×D811yescharacteristic
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223Dic22—41no—
224Dic22—41no—
225Dic22—82no—
226C8×C11—21no—
227C8×C11C2×#4111yescharacteristic
228C8×C11C2×#4111yescharacteristic
229C11⋊C8—21no—
230C11⋊C8—21no—
231C2×#135C2×D1111yescharacteristic
232#533—221no—
233C4×#41—221no—
234C2×Q32—111no—
235C2×Q32C2×D1111yescharacteristic
236C2×SD32—111no—
237C2×SD32C2×D1111yescharacteristic
238#500—111no—
239#494—111no—
240#487—221no—
241#467—111no—
242#467—221no—
243#467C2×D1111yescharacteristic
244C4×Q16—111no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×Q16—221no—
249C4×SD16—221no—
250C4×SD16—221no—
251C4×D8—111no—
252C4×D8—111no—
253#427—111no—
254#416—221no—
255C2×C4×C8—111no—
256#367—111no—
257#367—111no—
258#366—111no—
259#366—111no—
260C4⋊C16—111no—
261C4⋊C16—111no—
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#358C2×D1111yescharacteristic
268#357—111no—
269#357C2×D1111yescharacteristic
270C22⋊C16—111no—
271C22⋊C16C2×D1111yescharacteristic
272#346—111no—
273#346—111no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—42no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11C22×D811yescharacteristic
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#52511yescharacteristic
286C4×C11#57511yescharacteristic
287Dic11—21no—
288Dic11—21no—
289Dic11—21no—
290Dic11—81no—
291Dic11—81no—
292Dic11—81no—
293Dic11—81no—
294Dic11#51012yes—
295C2×#41—21no—
296#135—22no—
297#135—22no—
298C2×Q16—111no—
299C2×Q16—221no—
300C2×Q16C22×D1111yescharacteristic
301C2×Q16C22×D1111yescharacteristic
302C2×SD16—21no—
303C2×D8C22×D1111yescharacteristic
304C22×C8—111no—
305C22×C8C22×D1111yescharacteristic
306C4⋊Q8—221no—
307C4⋊Q8—221no—
308#125—441no—
309C22⋊Q8—21no—
310C22⋊Q8—221no—
311C22⋊Q8—441no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×Q8—441no—
317C4×D4—221no—
318C4×D4—221no—
319C4×D4—441no—
320C4×D4—441no—
321#117—221no—
322#117—441no—
323#117—441no—
324C2×C42—111no—
325C2×C42—441no—
326Q32—22no—
327Q32—222no—
328SD32—22no—
329SD32—222no—
330C2×C16—111no—
331C2×C16—111no—
332C2×C16C22×D1111yescharacteristic
333C2×C16C22×D1111yescharacteristic
334#107—111no—
335#107—111no—
336#107—111no—
337#107—221no—
338#107C22×D1111yescharacteristic
339#106—221no—
340#103—21no—
341#103—221no—
342#103—221no—
343#103—221no—
344#103—221no—
345#103—221no—
346#102—221no—
347#102—221no—
348C4×C8—111no—
349C4×C8—111no—
350C4×C8—111no—
351C4×C8—111no—
352C2×C11—41no—
353C2×C11—82no—
354C2×C11#310011yescharacteristic
355C2×C11C2×#51011yescharacteristic
356C2×C11#341411yescharacteristic
357#41—24no—
358#41—42no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—221no—
362C2×Q8—441no—
363C2×D4—21no—
364C2×D4—41no—
365C22×C4—41no—
366C22×C4—111no—
367C22×C4—111no—
368C22×C4—441no—
369C22×C4—441no—
370C22×C4D4×D1111yescharacteristic
371Q16—21no—
372Q16—21no—
373Q16—21no—
374Q16—221no—
375Q16—221no—
376Q16—442no—
377Q16#434112yes—
378SD16—24no—
379D8—21no—
380D8#434112yes—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—111no—
384C2×C8—111no—
385C2×C8—441no—
386C2×C8D4×D1111yescharacteristic
387C2×C8C23×D1111yescharacteristic
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
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—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C42—111no—
407C42—111no—
408C42—111no—
409C42—111no—
410C42—441no—
411C42—441no—
412C42—441no—
413C42—441no—
414C42—441no—
415C16—21no—
416C16—21no—
417C16—221no—
418C16—221no—
419C11#3367611yescharacteristic, complemented, Sylow
420C23—41no—
421C23D8×D1111yescharacteristic
422Q8—22no—
423Q8—41no—
424Q8—41no—
425Q8—41no—
426Q8—441no—
427Q8—441no—
428Q8—882no—
429D4—22no—
430D4—44no—
431D4—41no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—111no—
439C2×C4—111no—
440C2×C4—111no—
441C2×C4—111no—
442C2×C4—222no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—882no—
449C2×C4—882no—
450C2×C4D8×D1111yescharacteristic
451C2×C4C2×D4×D1111yescharacteristic
452C8—21no—
453C8—221no—
454C8—221no—
455C8C2×#434111yescharacteristic
456C8C2×#434111yescharacteristic
457C22—21no—
458C22—21no—
459C22—21no—
460C22—42no—
461C22—81no—
462C22—81no—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—42no—
466C4—81no—
467C4—81no—
468C4—112no—
469C4—221no—
470C4—221no—
471C4—221no—
472C4—881no—
473C4—881no—
474C4—881no—
475C4—881no—
476C4#1062311711yescharacteristic
477C4#1062330411yescharacteristic
478C2—41no—
479C2—82no—
480C2#1307861111yescharacteristic
481C2D11×#51011yescharacteristic
482C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2189C2
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
hypercenter#2189D11
hypocenterC11#33676
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2189

Complements

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

NH ≅ G/Ntype
1. #13079197C2semidirect
3. #13070825C2semidirect
4. #13070821C2semidirect
5. #13070766C2semidirect
6. #13070761C2semidirect
7. #13070664C2semidirect
8. #13070659C2semidirect
10. #13070487C2semidirect
11. #13070484C2semidirect
12. #13070481C2semidirect
13. #13070477C2semidirect
14. #13070416C2semidirect
419. C11#33676semidirect

Maximal subgroups

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

subgroupindex
#130791972
#135×Dic112
#130708252
#130708212
#130707662
#130707612
#130706642
#130706592
#130705562
#130704872
#130704842
#130704812
#130704772
#130704162
C11×#21892
#3367611