Finite Group Databasebeta

← #14908355

Subgroups — #14908355

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081718C211yesmaximal, characteristic, complemented
2#13078332C211yesmaximal, characteristic, complemented
3C2×#10622773C211yesmaximal, characteristic, complemented
4#13070743C214yesmaximal, complemented
5#13070733C214yesmaximal, complemented
6#13070411C211yesmaximal, characteristic, complemented
7#13070365C211yesmaximal, characteristic, complemented
8C2×#10622201C211yesmaximal, characteristic, complemented
9C2×C11×#509C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11C22×C11×D8C2211yescharacteristic
12#10623353—21no—
13C2×#66985—21no—
14C2×#66954C2211yescharacteristic
15C11×#509—22no—
16C11×#509—22no—
17C2×C11×SD32C2212yescomplemented
18C2×C11×D16C2212yescomplemented
19C2×C11×M32C2211yescharacteristic
20#10622850—21no—
21C2×#66897—21no—
22#10622805C2212yescomplemented
23#10622790—22no—
24#10622773—22no—
25#10622773C2214yes—
26#10622773C2212yescomplemented
27C2×#66883C2211yescharacteristic
28C2×#66883C2211yescharacteristic
29C2×#66876C2211yescharacteristic
30#10622520—22no—
31D11×M32—22no—
32#10622514C2214yescomplemented
33#10622203C2212yescomplemented
34#10622201C2214yescomplemented
35#10622201C2212yescomplemented
36#10622144C2214yescomplemented
37C2×C11×#41—21no—
38C22×D4×C11—21no—
39C2×#4339D411yescharacteristic
40C11×#135—21no—
41C11×#135—21no—
42C11×#135—21no—
43C11×#135—21no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8—21no—
47C2×C11×D8—21no—
48C2×C11×D8—21no—
49C2×C11×D8—21no—
50C2×C11×D8—21no—
51C2×C11×D8C2311yescharacteristic
52C2×C11×D8C2312yes—
53C22×C8×C11C2311yescharacteristic
54#67004—41no—
55#67003—42no—
56#67002—41no—
57#66995—22no—
58C2×#4324—41no—
59#66985—24no—
60#66985—22no—
61#66985—42no—
62C2×#4323—41no—
63C2×#4318—21no—
64C2×#4318—21no—
65C2×#4318D411yescharacteristic
66#66954—21no—
67#66954—21no—
68#66954D412yes—
69#66954C2312yes—
70C2×#4313—21no—
71C2×C8×D11—21no—
72C11×SD32—24no—
73C11×D16—24no—
74C11×M32D412yes—
75C11×M32D412yes—
76C2×C11×C16C2312yes—
77#66900—22no—
78#66897—24no—
79#66897—22no—
80#66883—21no—
81#66883—21no—
82#66883C2312yes—
83#66883C2312yes—
84#66876—21no—
85#66876C2312yes—
86C2×C11⋊C16—21no—
87#66862—24no—
88C16×D11—24no—
89#33618—111nomaximal, Sylow
90C24×C11—41no—
91C11×#41—41no—
92C11×#41—41no—
93C11×#41—41no—
94C11×#41—41no—
95C2×Q8×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C2×C22⋊D11—21no—
107#4339—21no—
108#4339—21no—
109#4339D812yes—
110#4339C2×D412yes—
111C2×D44D811yescharacteristic
112C2×C4×D11—21no—
113C2×Dic22D811yescharacteristic
114C11×Q16—21no—
115C11×Q16—21no—
116C11×SD16—41no—
117C11×SD16—41no—
118C11×D8—21no—
119C11×D8—22no—
120C11×D8—22no—
121C11×D8—21no—
122C11×D8—41no—
123C11×D8—41no—
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11#4111yescharacteristic
128C2×C8×C11#4111yescharacteristic
129C2×C8×C11C2411yescharacteristic
130#4326—42no—
131#4325—42no—
132#4324—44no—
133#4324—42no—
134#4323—44no—
135#4323—42no—
136#4318—21no—
137#4318—22no—
138#4318—22no—
139#4318—41no—
140#4318—41no—
141#4318C2×D412yes—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145#4313—22no—
146#4313—22no—
147C8×D11—22no—
148C8×D11—22no—
149C11×C16C2×D414yes—
150C11⋊C16—22no—
151C2×#509D1111yescharacteristic, complemented
152#3407—111no—
153#3067—111no—
154C2×#472—111no—
155#2223—114no—
156#2221—114no—
157#2161—111no—
158#2148—111no—
159C2×#361—111no—
160C23×C11—41no—
161C23×C11—42no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11—162no—
165C23×C11#13511yescharacteristic
166C22×D11—21no—
167Q8×C11—41no—
168Q8×C11—41no—
169D4×C11—42no—
170D4×C11—41no—
171D4×C11—42no—
172D4×C11—41no—
173D4×C11—81no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11—81no—
177C2×C4×C11—41no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11#13511yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—22no—
187C22⋊D11—22no—
188C2×Dic11—21no—
189D44—21no—
190D44C2×D812yes—
191C4×D11—22no—
192C4×D11—22no—
193Dic22—21no—
194Dic22C2×D812yes—
195C8×C11#12111yescharacteristic
196C8×C11#12111yescharacteristic
197C8×C11C22×D411yescharacteristic
198C8×C11C2×#4111yescharacteristic
199C11⋊C8—22no—
200C11⋊C8—42no—
201C11⋊C8—42no—
202#575—221no—
203C2×AGL(1,ℤ/8)—221no—
204C2×#135C2×D1111yescharacteristic
205C22×D8C2×D1111yescharacteristic
206C2×#131—111no—
207#509—22no—
208#509—22no—
209C2×SD32C2×D1112yescomplemented
210C2×D16C2×D1112yescomplemented
211#504—114no—
212#504—222no—
213C2×M32—111no—
214C2×M32—222no—
215C2×M32C2×D1111yescharacteristic
216#473—112no—
217#472—114no—
218#472—112no—
219#472—222no—
220#471—222no—
221C2×#108—111no—
222C2×#108—111no—
223#413—221no—
224C2×#100—221no—
225#368—114no—
226#362—112no—
227#361—114no—
228#361—112no—
229C22×C11—41no—
230C22×C11—81no—
231C22×C11—82no—
232C22×C11—161no—
233C22×C11—162no—
234C22×C11—162no—
235C22×C11—162no—
236C22×C11#46611yescharacteristic
237C22×C11#46611yescharacteristic
238C22×C11C2×#13511yescharacteristic
239C2×D11—22no—
240C2×D11—81no—
241C4×C11—81no—
242C4×C11#46611yescharacteristic
243C4×C11#46611yescharacteristic
244C4×C11C2×#12111yescharacteristic
245C4×C11C22×D811yescharacteristic
246Dic11—22no—
247C2×#41—21no—
248C2×#41—111no—
249C22×D4—21no—
250#137—222no—
251#137—441no—
252AGL(1,ℤ/8)—224no—
253AGL(1,ℤ/8)—222no—
254AGL(1,ℤ/8)—442no—
255AGL(1,ℤ/8)—441no—
256#135—21no—
257#135—21no—
258#135—21no—
259#135—21no—
260#135—442no—
261C2×Q16C22×D1111yescharacteristic
262C2×SD16—21no—
263C2×SD16—441no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—441no—
270C2×D8C22×D1112yes—
271C2×D8C22×D1111yescharacteristic
272#131—112no—
273#131—112no—
274#131—221no—
275#131—221no—
276C2×M16—111no—
277C2×M16—221no—
278C2×M16—221no—
279C2×M16—221no—
280C22×C8—221no—
281C22×C8C22×D1111yescharacteristic
282SD32—24no—
283D16—24no—
284M32—112no—
285M32—221no—
286M32—224no—
287M32C22⋊D1112yes—
288M32C22⋊D1112yes—
289C2×C16—221no—
290C2×C16—224no—
291C2×C16C22×D1112yes—
292#108—112no—
293#108—112no—
294#108—221no—
295#108—221no—
296#101—222no—
297#100—224no—
298#100—222no—
299C2×C11—21no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—161no—
303C2×C11—162no—
304C2×C11C2×#46611yescharacteristic
305D11—42no—
306C24—41no—
307#41—41no—
308#41—41no—
309#41—41no—
310#41—41no—
311#41—112no—
312#41—112no—
313#41—221no—
314#41—221no—
315C2×Q8—21no—
316C2×Q8—111no—
317C2×D4—22no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—111no—
326C2×D4—221no—
327C22×C4—41no—
328C22×C4—221no—
329C22×C4D4×D1111yescharacteristic
330Q16—21no—
331Q16—21no—
332Q16—442no—
333SD16—41no—
334SD16—41no—
335SD16—444no—
336SD16—442no—
337SD16—442no—
338D8—22no—
339D8—21no—
340D8—21no—
341D8—22no—
342D8—41no—
343D8—41no—
344D8—444no—
345D8—442no—
346M16—112no—
347M16—221no—
348M16—222no—
349M16—222no—
350M16—222no—
351M16—222no—
352M16—441no—
353M16—441no—
354C2×C8—221no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—441no—
358C2×C8—441no—
359C2×C8D4×D1111yescharacteristic
360C2×C8#434111yescharacteristic
361C2×C8#434111yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C16—222no—
366C16C2×C22⋊D1114yes—
367C11#3361811yescharacteristic, complemented, Sylow
368C23—41no—
369C23—42no—
370C23—81no—
371C23—81no—
372C23—162no—
373C23—221no—
374C23#6696511yescharacteristic
375Q8—41no—
376Q8—41no—
377Q8—112no—
378Q8—221no—
379D4—42no—
380D4—41no—
381D4—42no—
382D4—41no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—112no—
388D4—222no—
389D4—222no—
390D4—221no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—221no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4D8×D1111yescharacteristic
398C2×C4D8×D1111yescharacteristic
399C2×C4#6696511yescharacteristic
400C2×C4#6699111yescharacteristic
401C2×C4#6699111yescharacteristic
402C2×C4C2×D4×D1111yescharacteristic
403C8—222no—
404C8—442no—
405C8—442no—
406C8#6699111yescharacteristic
407C8#6699111yescharacteristic
408C8C2×#434111yescharacteristic
409C8C22×C22⋊D1111yescharacteristic
410C22—41no—
411C22—81no—
412C22—82no—
413C22—162no—
414C22—161no—
415C22—162no—
416C22—162no—
417C22—222no—
418C22—881no—
419C22#1062277011yescharacteristic
420C22#1062277011yescharacteristic
421C22C2×#6696511yescharacteristic
422C4—81no—
423C4—222no—
424C4#1062277011yescharacteristic
425C4#1062277011yescharacteristic
426C4C2×D8×D1111yescharacteristic
427C4C2×#6699111yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—162no—
432C2—161no—
433C2—442no—
434C2C2×#1062277011yescharacteristic
subgroupG/H
centerC2C2×#10622770
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#509C2
socleC2×C11C2×#466
hypercenterC2×#509D11
hypocenterC11#33618
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. #13081718C2semidirect
2. #13078332C2semidirect
3. C2×#10622773C2semidirect
4. #13070743C2semidirect
5. #13070733C2semidirect
6. #13070411C2semidirect
7. #13070365C2semidirect
8. C2×#10622201C2semidirect
9. C2×C11×#509C2semidirect
17. C2×C11×SD32C22semidirect
18. C2×C11×D16C22semidirect
22. #10622805C22semidirect
26. #10622773C22semidirect
32. #10622514C22semidirect
33. #10622203C22semidirect
34. #10622201C22semidirect
35. #10622201C22semidirect
36. #10622144C22semidirect
151. C2×#509D11semidirect
209. C2×SD32C2×D11semidirect
210. C2×D16C2×D11semidirect
367. C11#33618semidirect

Maximal subgroups

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

subgroupindex
#130817182
#130783322
C2×#106227732
#130707432
#130707332
#130704112
#130703652
C2×#106222012
C2×C11×#5092
#3361811