Finite Group Databasebeta

← #14908437

Subgroups — #14908437

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079127C211yesmaximal, characteristic
2C4×Q16×D11C211yesmaximal, characteristic
3#13070779C212yesmaximal, complemented
4#13070778C212yesmaximal, complemented
5#13070765C211yesmaximal, characteristic, complemented
6#13070759C211yesmaximal, characteristic, complemented
7#13070758C211yesmaximal, characteristic, complemented
8#13070401C212yesmaximal
9#13070370C211yesmaximal, characteristic
10#13070334C212yesmaximal
11C11×#2227C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2211yescharacteristic
13#10623259—21no—
14C4×Q8×D11—21no—
15C11×#500C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17Q16×Dic11C2211yescharacteristic
18#10622692—21no—
19C4×#4326—21no—
20C2×#66862C2212yes—
21#10622493—21no—
22#10622493C2212yes—
23D11×#107C2211yescharacteristic
24#10622491—21no—
25#10622491C2212yes—
26#10622486C2211yescharacteristic
27D11×#103—21no—
28#10622403—21no—
29C4×Dic44C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622295C2211yescharacteristic
32C11×#366C2212yes—
33C11×C4⋊C16C2211yescharacteristic
34C11×#358C2212yes—
35#10622202C2212yes—
36#10622143C2212yes—
37#10622141C2212yes—
38Dic11⋊C16C2212yes—
39#10622130C2212yes—
40#10622128C2212yes—
41#10622127C2212yes—
42C4⋊(C11⋊C16)C2211yescharacteristic
43C2×Q8×D11—21no—
44C2×C11×Q16C2311yescharacteristic
45C11×C4⋊Q8—21no—
46C4×Q8×C11—21no—
47#66999—41no—
48Q8×Dic11—21no—
49Q8×Dic11—41no—
50C2×#4326—21no—
51Q16×D11—22no—
52Q16×D11Q814yescomplemented
53C2×Dic44C2311yescharacteristic
54C2×C8×D11D411yescharacteristic
55C2×C8×D11C2311yescharacteristic
56#66950—41no—
57#66945—22no—
58C4⋊C4×D11—21no—
59C4⋊C4×D11—41no—
60#66943—22no—
61#66940—21no—
62#66940—41no—
63#66940—41no—
64C42×D11—41no—
65C42×D11D411yescharacteristic
66#66922—21no—
67C4×Dic22—21no—
68C4×Dic22—41no—
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2311yescharacteristic
73C11×#103—21no—
74C4×C8×C11C2311yescharacteristic
75#66899—21no—
76#66882—21no—
77#66882C2312yes—
78#66882C2311yescharacteristic
79#66880—21no—
80C8×Dic11D411yescharacteristic
81C8×Dic11C2311yescharacteristic
82C2×C11⋊C16C2312yes—
83#66874—21no—
84#66872—22no—
85#66872—22no—
86#66871—21no—
87C4×C11⋊C8D411yescharacteristic
88#66862—24no—
89#33628—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11—41no—
92Q8×D11—24no—
93Q8×D11—42no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C4×D11D811yescharacteristic
97C2×C4×D11D811yescharacteristic
98C2×C4×D11C2×D411yescharacteristic
99C2×Dic22—21no—
100C2×Dic22—41no—
101C2×Dic22—41no—
102C11×Q16—21no—
103C11×Q16C2×Q812yes—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2411yescharacteristic
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112#4326—24no—
113(C2×D11)⋊C4—42no—
114C4⋊Dic11—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—41no—
117C4⋊Dic11—42no—
118C4⋊Dic11—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—42no—
122Dic11⋊C4—41no—
123C4×Dic11—41no—
124C4×Dic11—41no—
125C4×Dic11—42no—
126C4×Dic11—41no—
127C4×Dic11D811yescharacteristic
128C4×Dic11D811yescharacteristic
129C4×Dic11C2×D411yescharacteristic
130C2×C11⋊C8C2×D411yescharacteristic
131C2×C11⋊C8C2×D411yescharacteristic
132Dic44—21no—
133Dic44C2×Q812yes—
134C8×D11—22no—
135C8×D11C2×Q812yes—
136C8×D11#4112yes—
137C11×C16—22no—
138C11⋊C16—22no—
139#3160—111no—
140C2×C4×Q16—111no—
141#2229—112no—
142#2229—112no—
143#2227—111no—
144#2227D1111yescharacteristic, complemented
145#2225—111no—
146#2225—111no—
147#2159—112no—
148#2150—111no—
149#2141—112no—
150C22×D11C2×D811yescharacteristic
151Q8×C11—22no—
152Q8×C11—41no—
153Q8×C11—82no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11C2×D811yescharacteristic
164C2×Dic11C2×D811yescharacteristic
165C2×Dic11C2×D811yescharacteristic
166C4×D11—22no—
167C4×D11—41no—
168C4×D11—44no—
169C4×D11—82no—
170C4×D11C22⋊Q812yes—
171C4×D11#13712yes—
172Dic22—22no—
173Dic22—41no—
174Dic22—44no—
175Dic22—82no—
176C8×C11—21no—
177C8×C11C22×Q811yescharacteristic
178C8×C11C2×#4111yescharacteristic
179C11⋊C8—21no—
180C11⋊C8C22⋊Q812yes—
181C22×Q16—111no—
182#533—221no—
183C2×C4×Q8—221no—
184C2×M32—112no—
185#500—111no—
186#500C2×D1111yescharacteristic
187#499—112no—
188#499—221no—
189#498—221no—
190C4×Q16—111no—
191C4×Q16—111no—
192C4×Q16—111no—
193C4×Q16—221no—
194C4×Q16—221no—
195C4×Q16C2×D1111yescharacteristic
196#427—112no—
197#427—221no—
198C2×#107—111no—
199C2×#103—221no—
200C2×C4×C8—111no—
201#367—112no—
202#367—112no—
203#366—112no—
204#366C2×D1112yes—
205C4⋊C16—112no—
206C4⋊C16—111no—
207C4⋊C16C2×D1111yescharacteristic
208#358—112no—
209#358—112no—
210#358—112no—
211#358C2×D1112yes—
212C22×C11C22×D811yescharacteristic
213C2×D11—21no—
214C2×D11—21no—
215C2×D11#47412yes—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11#51012yes—
221C4×C11C2×C22⋊Q811yescharacteristic
222C4×C11C2×#13711yescharacteristic
223Dic11—21no—
224Dic11—21no—
225Dic11—42no—
226Dic11—82no—
227Dic11—81no—
228Dic11#47412yes—
229C22×Q8—221no—
230C2×Q16—114no—
231C2×Q16—111no—
232C2×Q16—222no—
233C2×Q16—221no—
234C2×Q16C22×D1111yescharacteristic
235C22×C8—111no—
236C22×C8—111no—
237C4⋊Q8—21no—
238C4⋊Q8—221no—
239#125—222no—
240C22⋊Q8—441no—
241C22⋊Q8—441no—
242C4×Q8—21no—
243C4×Q8—221no—
244C4×Q8—221no—
245C4×Q8—221no—
246C4×Q8—441no—
247C4×Q8—441no—
248C4×Q8—441no—
249C4×Q8—441no—
250#117—222no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—441no—
253C2×C42—111no—
254C2×C42—441no—
255M32—224no—
256C2×C16—112no—
257C2×C16C22×D1112yes—
258#107—21no—
259#107—112no—
260#107—111no—
261#107—221no—
262#107—221no—
263#107C22×D1112yes—
264#107C22×D1111yescharacteristic
265#106—222no—
266#106—222no—
267#103—21no—
268#103—221no—
269#103—221no—
270#103—221no—
271C4×C8—111no—
272C4×C8—111no—
273C4×C8—111no—
274C4×C8C22×D1111yescharacteristic
275C2×C11C2×#47411yescharacteristic
276C2×C11C2×#51011yescharacteristic
277C2×C11#341411yescharacteristic
278D11—22no—
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8—224no—
282C2×Q8—221no—
283C2×Q8—441no—
284C2×Q8—442no—
285C2×Q8—441no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—441no—
290C22×C4—441no—
291Q16—21no—
292Q16—112no—
293Q16—224no—
294Q16—221no—
295Q16Q8×D1112yes—
296C2×C8—111no—
297C2×C8—112no—
298C2×C8—112no—
299C2×C8—111no—
300C2×C8—222no—
301C2×C8D4×D1111yescharacteristic
302C2×C8C23×D1111yescharacteristic
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—221no—
308C4⋊C4—222no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C22⋊C4—442no—
317C42—41no—
318C42—111no—
319C42—111no—
320C42—111no—
321C42—441no—
322C42—441no—
323C42—442no—
324C42—441no—
325C42D4×D1111yescharacteristic
326C16—22no—
327C16—222no—
328C11#3362811yescharacteristic, complemented, Sylow
329C23—111no—
330Q8—22no—
331Q8—41no—
332Q8—82no—
333Q8—222no—
334Q8—444no—
335Q8—441no—
336Q8—882no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—111no—
341C2×C4—112no—
342C2×C4—112no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—222no—
346C2×C4—441no—
347C2×C4—444no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—442no—
351C2×C4—882no—
352C2×C4D8×D1111yescharacteristic
353C2×C4D8×D1111yescharacteristic
354C2×C4C2×D4×D1111yescharacteristic
355C8—21no—
356C8—112no—
357C8—221no—
358C8C2×Q8×D1111yescharacteristic
359C8#41×D1111yescharacteristic
360C22—112no—
361C22—221no—
362C22—221no—
363C22C2×D8×D1111yescharacteristic
364C4—21no—
365C4—42no—
366C4—81no—
367C4—82no—
368C4—112no—
369C4—221no—
370C4—221no—
371C4—442no—
372C4—882no—
373C4—881no—
374C4#1062253112yes—
375C4D11×C22⋊Q811yescharacteristic
376C4D11×#13711yescharacteristic
377C2—222no—
378C2D11×#47411yescharacteristic
379C2C2×#1062253111yescharacteristic
380C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2227C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2227D11
hypocenterC11#33628
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. #13070779C2semidirect
4. #13070778C2semidirect
5. #13070765C2semidirect
6. #13070759C2semidirect
7. #13070758C2semidirect
11. C11×#2227C2semidirect
52. Q16×D11Q8semidirect
144. #2227D11semidirect
328. C11#33628semidirect

Maximal subgroups

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

subgroupindex
#130791272
C4×Q16×D112
#130707792
#130707782
#130707652
#130707592
#130707582
#130704012
#130703702
#130703342
C11×#22272
#3362811