Finite Group Databasebeta

← #14908609

Subgroups — #14908609

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622500C211yesmaximal, characteristic
2D11×#427C211yesmaximal, characteristic
3#13070827C212yesmaximal, complemented
4#13070826C212yesmaximal, complemented
5#13070820C212yesmaximal, complemented
6#13070815C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic, complemented
8#13070337C211yesmaximal, characteristic, complemented
9#13070335C211yesmaximal, characteristic, complemented
10#13070226C211yesmaximal, characteristic
11C11×#2159C211yesmaximal, characteristic, complemented
12C22×Dic44C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14D11×#117—21no—
15C2×#66950—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622719C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622611—21no—
22C2×#66874—21no—
23#10622500—21no—
24#10622500—21no—
25#10622500C2212yes—
26#10622500C2212yes—
27#10622493C2211yescharacteristic
28#10622493C2211yescharacteristic
29D11×#107C2211yescharacteristic
30D11×#107C2211yescharacteristic
31#10622473—21no—
32D11×#106—21no—
33C11×#367C2212yescomplemented
34C11×#366C2212yescomplemented
35(C2×D11)⋊C16C2212yes—
36(C2×D11)⋊C16C2212yes—
37#10622141C2212yescomplemented
38#10622141C2212yescomplemented
39#10622130C2212yescomplemented
40#10622130C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C22×C4×D11D411yescharacteristic
44C22×Dic22—21no—
45C22×C8×C11C2311yescharacteristic
46C11×#117—21no—
47C2×C11×C4⋊C4—21no—
48C2×(C2×D11)⋊C4—41no—
49#66979—21no—
50C2×C4⋊Dic11—41no—
51C22×C11⋊C8D411yescharacteristic
52C2×Dic44—22no—
53C2×Dic44—22no—
54C2×Dic44—21no—
55C2×Dic44C2312yes—
56C2×C8×D11—22no—
57C2×C8×D11—22no—
58C2×C8×D11D411yescharacteristic
59C2×C8×D11D411yescharacteristic
60C2×C8×D11C2311yescharacteristic
61C2×C8×D11C2311yescharacteristic
62#66950—22no—
63#66950—22no—
64#66950—41no—
65#66950—41no—
66#66945—21no—
67#66945—21no—
68C4⋊C4×D11—21no—
69C4⋊C4×D11—21no—
70C22⋊C4×D11—41no—
71#66930—41no—
72#66925—41no—
73C42×D11—41no—
74C11×M32—22no—
75C2×C11×C16C2312yes—
76C11×#107—21no—
77C11×#107C2311yescharacteristic
78C11×#107C2311yescharacteristic
79C11×#107C2312yes—
80C11×#106—21no—
81#66882C2311yescharacteristic
82#66882C2311yescharacteristic
83#66881—21no—
84#66876—22no—
85C2×C11⋊C16C2312yes—
86#66874—22no—
87#66874—22no—
88#66872—21no—
89#66872—21no—
90#66871—21no—
91#66871—21no—
92#33649—111nomaximal, Sylow
93C23×D11D811yescharacteristic
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×Dic11—41no—
97C22×Dic11D811yescharacteristic
98C2×C4×D11—22no—
99C2×C4×D11—22no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11D811yescharacteristic
103C2×C4×D11D811yescharacteristic
104C2×C4×D11C2×D411yescharacteristic
105C2×C4×D11C2×D411yescharacteristic
106C2×Dic22—22no—
107C2×Dic22—42no—
108C2×Dic22—41no—
109C2×Dic22—42no—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11#4112yes—
112C2×C8×C11#4112yes—
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—41no—
120C22⋊Dic11—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—42no—
124(C2×D11)⋊C4—42no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—42no—
128C4⋊Dic11—42no—
129Dic11⋊C4—41no—
130Dic11⋊C4—41no—
131C4×Dic11—41no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137Dic44—22no—
138Dic44—22no—
139Dic44—42no—
140C8×D11—22no—
141C8×D11—22no—
142C8×D11—21no—
143C8×D11—21no—
144C8×D11—21no—
145C8×D11—21no—
146C11×C16—22no—
147C11⋊C16—22no—
148C2×#467—111no—
149C2×#427—111no—
150#2237—112no—
151#2237—112no—
152#2236—112no—
153#2235—112no—
154#2159—111no—
155#2159D1111yescharacteristic, complemented
156#2141—111no—
157#2141—111no—
158#2112—111no—
159C23×C11C2×D811yescharacteristic
160C22×D11—22no—
161C22×D11—22no—
162C22×D11—41no—
163C22×D11C2×D811yescharacteristic
164C22×D11C2×D811yescharacteristic
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—82no—
169C2×C4×C11#12312yes—
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11#13712yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×Dic11—22no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—82no—
178C2×Dic11C2×D811yescharacteristic
179C2×Dic11C2×D811yescharacteristic
180C4×D11—21no—
181C4×D11—21no—
182C4×D11—21no—
183C4×D11—21no—
184C4×D11—22no—
185C4×D11—22no—
186C4×D11—82no—
187C4×D11—82no—
188Dic22—42no—
189Dic22—42no—
190Dic22—82no—
191C8×C11#12312yes—
192C8×C11C2×#4111yescharacteristic
193C8×C11C2×#4111yescharacteristic
194C11⋊C8—21no—
195C11⋊C8—21no—
196C22×Q16—111no—
197C23×C8—111no—
198C2×C22⋊Q8—221no—
199C2×#117—221no—
200C2×M32—111no—
201C2×M32C2×D1111yescharacteristic
202#467—112no—
203#467—112no—
204#467—221no—
205#467—221no—
206#427—111no—
207#427—111no—
208#427—111no—
209#427—221no—
210#427—221no—
211#427C2×D1111yescharacteristic
212C2×#107—111no—
213C2×#107—111no—
214C2×#107C2×D1111yescharacteristic
215C2×#106—221no—
216C2×#103—221no—
217#367—112no—
218#367C2×D1112yescomplemented
219#366—112no—
220#366C2×D1112yescomplemented
221#358—112no—
222#358—112no—
223#358—112no—
224#358—112no—
225C22⋊C16—112no—
226C22⋊C16—112no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11#48012yes—
230C22×C11C22×D811yescharacteristic
231C2×D11—21no—
232C2×D11—21no—
233C2×D11—21no—
234C2×D11—21no—
235C2×D11—21no—
236C2×D11—44no—
237C2×D11#51012yes—
238C4×C11—81no—
239C4×C11—82no—
240C4×C11—81no—
241C4×C11#48012yes—
242C4×C11C2×#12311yescharacteristic
243C4×C11C2×#13711yescharacteristic
244Dic11—21no—
245Dic11—21no—
246Dic11—82no—
247Dic11—81no—
248Dic11—81no—
249C22×Q8—221no—
250C23×C4—111no—
251C2×Q16—112no—
252C2×Q16—222no—
253C2×Q16—221no—
254C2×Q16—222no—
255C22×C8—111no—
256C22×C8—111no—
257C22×C8—111no—
258C22×C8—111no—
259C22×C8—111no—
260C22×C8—222no—
261C22×C8—222no—
262C22×C8C22×D1111yescharacteristic
263C22⋊Q8—222no—
264C22⋊Q8—222no—
265C22⋊Q8—441no—
266C22⋊Q8—441no—
267#117—21no—
268#117—221no—
269#117—221no—
270#117—221no—
271#117—441no—
272#117—441no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—441no—
277C2×C22⋊C4—441no—
278C2×C22⋊C4—441no—
279C2×C42—441no—
280M32—22no—
281M32—222no—
282C2×C16—112no—
283C2×C16C22×D1112yes—
284#107—21no—
285#107—111no—
286#107—111no—
287#107—221no—
288#107—221no—
289#107C22×D1111yescharacteristic
290#107C22×D1111yescharacteristic
291#107C22×D1112yes—
292#106—21no—
293#106—221no—
294#106—221no—
295#106—221no—
296#103—222no—
297#103—222no—
298C2×C11—22no—
299C2×C11C2×#48011yescharacteristic
300C2×C11C2×#51011yescharacteristic
301C2×C11#341411yescharacteristic
302D11—22no—
303D11—41no—
304C24—111no—
305C2×Q8—222no—
306C2×Q8—441no—
307C2×Q8—442no—
308C2×Q8—442no—
309C22×C4—41no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—441no—
318C22×C4—441no—
319C22×C4—441no—
320C22×C4D4×D1111yescharacteristic
321Q16—222no—
322Q16—222no—
323Q16—442no—
324C2×C8—111no—
325C2×C8—111no—
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—221no—
330C2×C8—221no—
331C2×C8—221no—
332C2×C8—221no—
333C2×C8#433912yes—
334C2×C8D4×D1111yescharacteristic
335C2×C8#434312yes—
336C2×C8C23×D1111yescharacteristic
337C4⋊C4—22no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C4⋊C4—442no—
346C4⋊C4—442no—
347C22⋊C4—41no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C22⋊C4—442no—
351C22⋊C4—442no—
352C22⋊C4—441no—
353C42—41no—
354C42—441no—
355C42—441no—
356C42—441no—
357C16—22no—
358C16—222no—
359C11#3364911yescharacteristic, complemented, Sylow
360C23—111no—
361C23—111no—
362C23—222no—
363C23—222no—
364C23—441no—
365C23D8×D1111yescharacteristic
366Q8—442no—
367Q8—442no—
368Q8—882no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—111no—
374C2×C4—111no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—442no—
385C2×C4—882no—
386C2×C4—882no—
387C2×C4—882no—
388C2×C4#6694712yes—
389C2×C4D8×D1111yescharacteristic
390C2×C4#6697112yes—
391C2×C4C2×D4×D1111yescharacteristic
392C8—221no—
393C8—221no—
394C8#6694712yes—
395C8C2×#433911yescharacteristic
396C8C2×#434311yescharacteristic
397C22—21no—
398C22—21no—
399C22—112no—
400C22—221no—
401C22—221no—
402C22—221no—
403C22—221no—
404C22—221no—
405C22—444no—
406C22#1062249512yes—
407C22C2×D8×D1111yescharacteristic
408C4—81no—
409C4—82no—
410C4—81no—
411C4—221no—
412C4—221no—
413C4—881no—
414C4—881no—
415C4—882no—
416C4#1062249512yes—
417C4C2×#6694711yescharacteristic
418C4C2×#6697111yescharacteristic
419C2—22no—
420C2—222no—
421C2—441no—
422C2C2×#1062249511yescharacteristic
423C2D11×#51011yescharacteristic
424C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC23×D11D8
hypercenter#2159D11
hypocenterC11#33649
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
3. #13070827C2semidirect
4. #13070826C2semidirect
5. #13070820C2semidirect
6. #13070815C2semidirect
7. #13070402C2semidirect
8. #13070337C2semidirect
9. #13070335C2semidirect
11. C11×#2159C2semidirect
33. C11×#367C22semidirect
34. C11×#366C22semidirect
37. #10622141C22semidirect
38. #10622141C22semidirect
39. #10622130C22semidirect
40. #10622130C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
155. #2159D11semidirect
218. #367C2×D11semidirect
220. #366C2×D11semidirect
359. C11#33649semidirect

Maximal subgroups

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

subgroupindex
C2×#106225002
D11×#4272
#130708272
#130708262
#130708202
#130708152
#130704022
#130703372
#130703352
#130702262
C11×#21592
#3364911