Finite Group Databasebeta

← #14908860

Subgroups — #14908860

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic, complemented
2C4×#66957C211yesmaximal, characteristic
3#13070825C212yesmaximal, complemented
4#13070769C211yesmaximal, characteristic, complemented
5#13070764C211yesmaximal, characteristic, complemented
6#13070667C211yesmaximal, characteristic, complemented
7#13070662C211yesmaximal, characteristic, complemented
8#13070558C212yesmaximal
9#13070488C212yesmaximal, complemented
10#13070482C212yesmaximal, complemented
11C11×#2163C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C4×#4339—21no—
14#10623001—21no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622729—21no—
17#10622729C2212yes—
18#10622726—21no—
19#10622719C2211yescharacteristic
20C2×Dic88C2212yes—
21C2×#66864C2212yes—
22#10622312C2211yescharacteristic
23C4×Dic44—21no—
24C4×Dic44C2211yescharacteristic
25C4×Dic44C2211yescharacteristic
26C4×Dic44C2212yes—
27C4×D88C2211yescharacteristic
28C4×D88C2211yescharacteristic
29C4×#4314—21no—
30C4×#4314—21no—
31#10622295C2211yescharacteristic
32#10622294—21no—
33C11×C4⋊C16C2211yescharacteristic
34C11×C4⋊C16C2211yescharacteristic
35C11×C22⋊C16C2212yes—
36C11×#346C2212yes—
37#10622147C2212yes—
38#10622143C2212yes—
39#10622142C2212yes—
40#10622141C2212yes—
41#10622141C2212yes—
42#10622141C2212yes—
43C2×#4339—21no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C42×C11D411yescharacteristic
47C4×C22⋊D11—41no—
48C4×C22⋊D11—41no—
49#66979—21no—
50#66979—41no—
51#66977—22no—
52#66977—41no—
53C2×Dic44—21no—
54C2×Dic44C2312yes—
55C2×Dic44C2311yescharacteristic
56#66957—22no—
57#66957—22no—
58C2×D88C2311yescharacteristic
59C2×#4314—21no—
60C4×D44—21no—
61C4×D44—21no—
62#66925—41no—
63C42×D11—41no—
64#66923—41no—
65#66922—21no—
66#66922—21no—
67C4×Dic22—22no—
68C4×Dic22—21no—
69C4×Dic22—21no—
70C4×Dic22—41no—
71C2×C11×C16C2312yes—
72C2×C11×C16C2312yes—
73C4×C8×C11D411yescharacteristic
74C4×C8×C11D411yescharacteristic
75C4×C8×C11C2311yescharacteristic
76C4×C8×C11C2311yescharacteristic
77#66885—21no—
78#66885—21no—
79#66882—21no—
80#66882C2312yes—
81#66882C2311yescharacteristic
82#66882C2311yescharacteristic
83#66881—21no—
84#66880—21no—
85#66880—21no—
86#66880—22no—
87#66880—22no—
88Dic88—24no—
89#66864—24no—
90#33676—111nomaximal, Sylow
91C22×C4×C11D811yescharacteristic
92C22×C4×C11D811yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—41no—
95#4339—24no—
96#4339—42no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×Dic22—21no—
102C2×Dic22—22no—
103C2×Dic22—41no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—41no—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2411yescharacteristic
111C42×C11D811yescharacteristic
112C42×C11D811yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C22⋊Dic11—42no—
116C22⋊Dic11—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—42no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128Dic11⋊C4—42no—
129C4×Dic11—42no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132C4×Dic11—41no—
133Dic44—21no—
134Dic44—22no—
135Dic44—22no—
136Dic44—42no—
137Dic44#4112yes—
138D88—21no—
139D88#4112yes—
140#4314—24no—
141C11×C16—22no—
142C11×C16—22no—
143#3170—111no—
144C4×#135—111no—
145#2237—112no—
146#2227—111no—
147#2226—111no—
148#2209—111no—
149#2208—111no—
150#2189—112no—
151#2176—112no—
152#2175—112no—
153#2163D1111yescharacteristic, complemented
154C23×C11C2×D811yescharacteristic
155C22×D11—41no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C22⋊D11—44no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172D44—22no—
173D44—41no—
174C4×D11—44no—
175C4×D11—82no—
176C4×D11—82no—
177Dic22—22no—
178Dic22—41no—
179Dic22—42no—
180Dic22—42no—
181Dic22—82no—
182C8×C11—21no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11C2×#4111yescharacteristic
186C8×C11C2×#4111yescharacteristic
187C2×#135—111no—
188#533—221no—
189C4×#41—221no—
190C2×Q32—112no—
191C2×SD32—112no—
192#500—111no—
193#494—111no—
194#487—221no—
195#467—112no—
196#467—221no—
197C4×Q16—112no—
198C4×Q16—111no—
199C4×Q16—111no—
200C4×Q16—221no—
201C4×SD16—221no—
202C4×SD16—221no—
203C4×D8—111no—
204C4×D8—111no—
205#427—111no—
206#416—221no—
207C2×C4×C8C2×D1111yescharacteristic
208#367—112no—
209#366—112no—
210C4⋊C16C2×D1111yescharacteristic
211C4⋊C16C2×D1111yescharacteristic
212#358—112no—
213#358—112no—
214#358—112no—
215#357—112no—
216C22⋊C16C2×D1112yes—
217#346C2×D1112yes—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11C22×D811yescharacteristic
222C2×D11—42no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11#51012yes—
230C4×C11#52511yescharacteristic
231C4×C11#57511yescharacteristic
232Dic11—42no—
233Dic11—82no—
234Dic11—81no—
235Dic11—82no—
236Dic11—81no—
237C2×#41—221no—
238#135—222no—
239#135—222no—
240C2×Q16—111no—
241C2×Q16—112no—
242C2×Q16—221no—
243C2×SD16—221no—
244C2×D8—111no—
245C22×C8D4411yescharacteristic
246C22×C8C22×D1111yescharacteristic
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249#125—441no—
250C22⋊Q8—222no—
251C22⋊Q8—441no—
252C4×Q8—221no—
253C4×Q8—221no—
254C4×Q8—222no—
255C4×Q8—441no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—441no—
259C4×D4—441no—
260#117—221no—
261#117—441no—
262#117—441no—
263C2×C42—441no—
264C2×C42D4411yescharacteristic
265Q32—224no—
266SD32—224no—
267C2×C16C22×D1112yes—
268C2×C16C22×D1112yes—
269#107—112no—
270#107—111no—
271#107—111no—
272#107—221no—
273#106—221no—
274#103—221no—
275#103—221no—
276#103—222no—
277#103—222no—
278#102—221no—
279#102—221no—
280C4×C8D4411yescharacteristic
281C4×C8D4411yescharacteristic
282C4×C8C22×D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C2×C11—41no—
285C2×C11#310011yescharacteristic
286C2×C11C2×#51011yescharacteristic
287C2×C11#341411yescharacteristic
288D11—82no—
289#41—224no—
290#41—442no—
291C2×Q8—221no—
292C2×Q8—222no—
293C2×Q8—441no—
294C2×D4—221no—
295C2×D4—441no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4D8811yescharacteristic
300C22×C4D8811yescharacteristic
301C22×C4C2×D4411yescharacteristic
302Q16—112no—
303Q16—221no—
304Q16—222no—
305Q16—222no—
306Q16—442no—
307SD16—224no—
308D8—112no—
309D8—221no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—41no—
313C2×C8C2×D4411yescharacteristic
314C2×C8C2×D4411yescharacteristic
315C2×C8C2×D4411yescharacteristic
316C2×C8C23×D1111yescharacteristic
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—222no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—442no—
325C4⋊C4—442no—
326C4⋊C4—441no—
327C22⋊C4—441no—
328C22⋊C4—442no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C42—441no—
332C42—441no—
333C42—441no—
334C42—442no—
335C42D8811yescharacteristic
336C42D8811yescharacteristic
337C42C2×D4411yescharacteristic
338C42C2×D4411yescharacteristic
339C16—22no—
340C16—22no—
341C11#3367611yescharacteristic, complemented, Sylow
342C23—441no—
343C23C2×D8811yescharacteristic
344Q8—222no—
345Q8—441no—
346Q8—442no—
347Q8—442no—
348Q8—882no—
349D4—222no—
350D4—444no—
351D4—441no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—444no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—882no—
363C2×C4—882no—
364C2×C4C2×D8811yescharacteristic
365C2×C4C2×D8811yescharacteristic
366C2×C4C2×D8811yescharacteristic
367C2×C4C2×D8811yescharacteristic
368C2×C4C2×D8811yescharacteristic
369C2×C4C22×D4411yescharacteristic
370C8—21no—
371C8—21no—
372C8—21no—
373C8#41×D1111yescharacteristic
374C8#41×D1111yescharacteristic
375C22—21no—
376C22—21no—
377C22—21no—
378C22—442no—
379C22—881no—
380C22—881no—
381C22C22×D8811yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—442no—
387C4—882no—
388C4—881no—
389C4—881no—
390C4—882no—
391C4#1062252212yes—
392C4#1062305511yescharacteristic
393C4#1062327911yescharacteristic
394C2—41no—
395C2—882no—
396C2#1307861711yescharacteristic
397C2C2×#1062252211yescharacteristic
398C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2163C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2163D11
hypocenterC11#33676
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
1. #13079202C2semidirect
3. #13070825C2semidirect
4. #13070769C2semidirect
5. #13070764C2semidirect
6. #13070667C2semidirect
7. #13070662C2semidirect
9. #13070488C2semidirect
10. #13070482C2semidirect
11. C11×#2163C2semidirect
153. #2163D11semidirect
341. C11#33676semidirect

Maximal subgroups

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

subgroupindex
#130792022
C4×#669572
#130708252
#130707692
#130707642
#130706672
#130706622
#130705582
#130704882
#130704822
C11×#21632
#3367611