Finite Group Databasebeta

← #14908468

Subgroups — #14908468

Order 2816.

520 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079149C211yesmaximal, characteristic
2#13077479C211yesmaximal, characteristic
3#13070782C211yesmaximal, characteristic, complemented
4#13070781C211yesmaximal, characteristic, complemented
5#13070780C211yesmaximal, characteristic, complemented
6#13070779C211yesmaximal, characteristic, complemented
7#13070767C211yesmaximal, characteristic, complemented
8#13070756C211yesmaximal, characteristic, complemented
9#13070755C211yesmaximal, characteristic, complemented
10#13070401C211yesmaximal, characteristic
11#13070397C211yesmaximal, characteristic
12#13070373C211yesmaximal, characteristic
13#13070334C211yesmaximal, characteristic
14D11×#358C211yesmaximal, characteristic
15C11×#2227C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17#10623260—21no—
18#10623103—21no—
19C11×#500C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22#10622693—21no—
23#10622643—21no—
24C2×#66862C2211yescharacteristic
25C2×C16×D11C2211yescharacteristic
26#10622494—21no—
27#10622493C2211yescharacteristic
28#10622493C2211yescharacteristic
29D11×#107C2211yescharacteristic
30#10622491C2211yescharacteristic
31#10622489—21no—
32#10622487C2211yescharacteristic
33#10622486C2211yescharacteristic
34#10622415—21no—
35#10622402—21no—
36C4×Dic44C2211yescharacteristic
37#10622302C2211yescharacteristic
38#10622296C2211yescharacteristic
39C11×#366C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622143C2211yescharacteristic
47#10622142C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×C11×Q16C2311yescharacteristic
61C11×C4⋊Q8—21no—
62C4×Q8×C11—21no—
63#66999—41no—
64Q8×Dic11—21no—
65#66997—41no—
66C2×#4326—21no—
67Q16×D11—22no—
68Q16×D11Q814yescomplemented
69C2×Dic44C2311yescharacteristic
70C2×#4313D411yescharacteristic
71C2×C8×D11C2311yescharacteristic
72#66949—41no—
73#66945—21no—
74#66945—21no—
75#66945—41no—
76C4⋊C4×D11—21no—
77#66943—21no—
78#66942—41no—
79#66941—21no—
80#66940—21no—
81#66940—41no—
82#66925—41no—
83#66925D411yescharacteristic
84#66923—21no—
85C4×Dic22—21no—
86C4×Dic22—41no—
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C11×#107—21no—
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#103—21no—
94C4×C8×C11C2311yescharacteristic
95#66899—21no—
96#66882C2311yescharacteristic
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66881—21no—
100#66880—21no—
101#66879D411yescharacteristic
102C8×Dic11C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104C2×C11⋊C16C2311yescharacteristic
105#66874—21no—
106#66872—21no—
107#66872—21no—
108#66872—21no—
109#66871—21no—
110#66871—21no—
111#66867D411yescharacteristic
112#66862—22no—
113C16×D11—22no—
114#33632—111nomaximal, Sylow
115C2×Q8×C11—21no—
116C2×Q8×C11—41no—
117Q8×D11—24no—
118Q8×D11—42no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×C4×D11C2×D411yescharacteristic
122C2×Dic22—21no—
123C2×Dic22—41no—
124C2×Dic22—41no—
125C11×Q16—21no—
126C11×Q16C2×Q812yes—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2411yescharacteristic
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C42×C11—41no—
135C42×C11C2×D411yescharacteristic
136#4326—24no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4D811yescharacteristic
140(C2×D11)⋊C4D811yescharacteristic
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146Dic11⋊C4—41no—
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4D811yescharacteristic
154Dic11⋊C4D811yescharacteristic
155C4×Dic11—41no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163Dic44—21no—
164Dic44C2×Q812yes—
165#4313—22no—
166C8×D11C2×Q812yes—
167C8×D11#4112yes—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3164—111no—
173#2950—111no—
174#2229—111no—
175#2229—111no—
176#2229—111no—
177#2229—111no—
178#2227—111no—
179#2227D1111yescharacteristic, complemented
180#2225—111no—
181#2225—111no—
182#2159—111no—
183#2158—111no—
184#2151—111no—
185#2141—111no—
186C2×#358—111no—
187C22×D11C2×D811yescharacteristic
188Q8×C11—22no—
189Q8×C11—41no—
190Q8×C11—161no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11C2×D811yescharacteristic
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205C4×D11—44no—
206C4×D11—161no—
207C4×D11C22⋊Q812yes—
208C4×D11#13712yes—
209Dic22—22no—
210Dic22—41no—
211Dic22—44no—
212Dic22—161no—
213C8×C11—21no—
214C8×C11C22×Q811yescharacteristic
215C8×C11C2×#4111yescharacteristic
216C11⋊C8—21no—
217C11⋊C8C22⋊Q812yes—
218C22×Q16—111no—
219#544—221no—
220#519—221no—
221C2×M32—111no—
222C22×C16—111no—
223#501—221no—
224#501—221no—
225#500—111no—
226#500C2×D1111yescharacteristic
227#499—111no—
228#499—111no—
229#441—221no—
230#441—221no—
231C4×Q16—111no—
232C4×Q16—111no—
233C4×Q16—111no—
234C4×Q16C2×D1111yescharacteristic
235#428—221no—
236#427—111no—
237#427—111no—
238C2×#107—111no—
239#419—221no—
240#405—111no—
241#367—111no—
242#367—111no—
243#367—111no—
244#367—111no—
245#366—111no—
246#366—111no—
247#366C2×D1111yescharacteristic
248#366C2×D1111yescharacteristic
249C4⋊C16—111no—
250C4⋊C16—111no—
251C4⋊C16—111no—
252C4⋊C16C2×D1111yescharacteristic
253#358—111no—
254#358—111no—
255#358—111no—
256#358—111no—
257#358—111no—
258#358—111no—
259#358C2×D1111yescharacteristic
260#358C2×D1111yescharacteristic
261C22×C11C22×D811yescharacteristic
262C2×D11—21no—
263C2×D11—21no—
264C2×D11#47412yes—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11C2×C22⋊Q811yescharacteristic
272C4×C11C2×#13711yescharacteristic
273Dic11—21no—
274Dic11—21no—
275Dic11—42no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279Dic11#47412yes—
280C22×Q8—221no—
281C2×Q16—114no—
282C2×Q16—111no—
283C2×Q16—222no—
284C2×Q16—221no—
285C2×Q16C22×D1111yescharacteristic
286C2×M16—111no—
287C22×C8—111no—
288C4⋊Q8—21no—
289C4⋊Q8—221no—
290C4⋊Q8—441no—
291#125—221no—
292#125—221no—
293#125—441no—
294C22⋊Q8—441no—
295C22⋊Q8—441no—
296C4×Q8—21no—
297C4×Q8—221no—
298C4×Q8—221no—
299C4×Q8—221no—
300C4×Q8—441no—
301C4×Q8—441no—
302#117—111no—
303#117—221no—
304#117—221no—
305#117—441no—
306#117—441no—
307C2×C4⋊C4—221no—
308M32—222no—
309C2×C16—111no—
310C2×C16—111no—
311C2×C16—222no—
312C2×C16C22×D1111yescharacteristic
313C2×C16C22×D1111yescharacteristic
314#107—21no—
315#107—111no—
316#107—111no—
317#107—111no—
318#107—221no—
319#107—221no—
320#107C22×D1111yescharacteristic
321#107C22×D1111yescharacteristic
322#107C22×D1111yescharacteristic
323#106—221no—
324#106—221no—
325#106—221no—
326#106—221no—
327#103—21no—
328#103—221no—
329#103—221no—
330#103—221no—
331#97—111no—
332#97—111no—
333C4×C8—111no—
334C4×C8C22×D1111yescharacteristic
335C2×C11C2×#47411yescharacteristic
336C2×C11#341611yescharacteristic
337C2×C11#341711yescharacteristic
338D11—22no—
339C2×Q8—21no—
340C2×Q8—41no—
341C2×Q8—224no—
342C2×Q8—221no—
343C2×Q8—441no—
344C2×Q8—441no—
345C2×Q8—442no—
346C22×C4—111no—
347C22×C4—441no—
348C22×C4—441no—
349Q16—21no—
350Q16—112no—
351Q16—224no—
352Q16—221no—
353Q16Q8×D1112yes—
354M16—222no—
355C2×C8—111no—
356C2×C8—112no—
357C2×C8—112no—
358C2×C8—111no—
359C2×C8D4×D1111yescharacteristic
360C2×C8C23×D1111yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—111no—
367C4⋊C4—111no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C22⋊C4—111no—
381C22⋊C4—111no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C42—41no—
385C42—111no—
386C42—441no—
387C42—441no—
388C42—441no—
389C42—441no—
390C42—441no—
391C42D4×D1111yescharacteristic
392C16—21no—
393C16—21no—
394C16—221no—
395C16—221no—
396C11#3363211yescharacteristic, complemented, Sylow
397C23—111no—
398Q8—22no—
399Q8—41no—
400Q8—161no—
401Q8—222no—
402Q8—444no—
403Q8—441no—
404Q8—1761no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—111no—
410C2×C4—112no—
411C2×C4—112no—
412C2×C4—111no—
413C2×C4—111no—
414C2×C4—444no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—1761no—
420C2×C4D8×D1111yescharacteristic
421C2×C4D8×D1111yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C8—21no—
424C8—112no—
425C8—221no—
426C8C2×Q8×D1111yescharacteristic
427C8#41×D1111yescharacteristic
428C22—112no—
429C22—221no—
430C22—221no—
431C22C2×D8×D1111yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—112no—
439C4—221no—
440C4—221no—
441C4—442no—
442C4—881no—
443C4—881no—
444C4—881no—
445C4D11×C22⋊Q811yescharacteristic
446C4D11×#13711yescharacteristic
447C2—222no—
448C2D11×#47411yescharacteristic
449C2#1308176211yescharacteristic
450C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2227C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2227D11
hypocenterC11#33632
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
3. #13070782C2semidirect
4. #13070781C2semidirect
5. #13070780C2semidirect
6. #13070779C2semidirect
7. #13070767C2semidirect
8. #13070756C2semidirect
9. #13070755C2semidirect
15. C11×#2227C2semidirect
68. Q16×D11Q8semidirect
179. #2227D11semidirect
396. C11#33632semidirect

Maximal subgroups

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

subgroupindex
#130791492
#130774792
#130707822
#130707812
#130707802
#130707792
#130707672
#130707562
#130707552
#130704012
#130703972
#130703732
#130703342
D11×#3582
C11×#22272
#3363211