Finite Group Databasebeta

← #14908421

Subgroups — #14908421

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079130C211yesmaximal, characteristic, complemented
2C4×#66957C211yesmaximal, characteristic
3#13070781C212yesmaximal, complemented
4#13070774C212yesmaximal, complemented
5#13070769C211yesmaximal, characteristic, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070759C211yesmaximal, characteristic, complemented
8#13070754C211yesmaximal, characteristic, complemented
9#13070400C212yesmaximal, complemented
10#13070324C212yesmaximal
11C2×C11×C4⋊C16C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C4×#4339—21no—
14#10623001—21no—
15C22×C11×C16C2212yes—
16C2×C4×C8×C11C2211yescharacteristic
17#10622726—21no—
18#10622719—21no—
19#10622719C2211yescharacteristic
20#10622719C2212yes—
21C4×Dic44C2211yescharacteristic
22C4×Dic44C2211yescharacteristic
23C4×D88C2211yescharacteristic
24C4×D88C2211yescharacteristic
25C4×#4314—21no—
26C4×#4314—21no—
27#10622296—21no—
28#10622296C2212yes—
29#10622295C2211yescharacteristic
30#10622295C2211yescharacteristic
31#10622293—21no—
32C11×C4⋊C16C2211yescharacteristic
33C11×C4⋊C16C2211yescharacteristic
34C11×C4⋊C16C2212yes—
35#10622147C2212yes—
36#10622147C2212yes—
37#10622143C2212yes—
38#10622143C2212yes—
39#10622142C2212yes—
40#10622142C2212yes—
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—22no—
51#66977—41no—
52#66977—41no—
53C2×Dic44C2311yescharacteristic
54#66957—22no—
55#66957Q814yescomplemented
56C2×D88C2311yescharacteristic
57C2×#4314—21no—
58C4×D44—21no—
59C4×D44—21no—
60#66925—41no—
61C42×D11—41no—
62#66923—22no—
63#66922—21no—
64#66922—21no—
65C4×Dic22—21no—
66C4×Dic22—21no—
67C4×Dic22—41no—
68C4×Dic22—41no—
69C2×C11×C16—24no—
70C2×C11×C16C2312yes—
71C2×C11×C16C2312yes—
72C4×C8×C11D411yescharacteristic
73C4×C8×C11D411yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76#66885—21no—
77#66885—21no—
78#66882—21no—
79#66882—21no—
80#66882C2312yes—
81#66882C2312yes—
82#66882C2311yescharacteristic
83#66882C2311yescharacteristic
84#66881—22no—
85#66881—22no—
86#66881—21no—
87#66880—21no—
88#66880—21no—
89#33626—111nomaximal, Sylow
90C22×C4×C11D811yescharacteristic
91C22×C4×C11D811yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94#4339—24no—
95#4339—42no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×C8×C11—22no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×Q812yes—
108C2×C8×C11#4112yes—
109C2×C8×C11C2411yescharacteristic
110C42×C11D811yescharacteristic
111C42×C11D811yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C22⋊Dic11—42no—
115C22⋊Dic11—41no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—42no—
127Dic11⋊C4—42no—
128C4×Dic11—41no—
129C4×Dic11—41no—
130C4×Dic11—42no—
131C4×Dic11—41no—
132Dic44—21no—
133Dic44C2×Q812yes—
134D88—21no—
135D88C2×Q812yes—
136#4314—24no—
137C11×C16—22no—
138C11×C16—22no—
139#3160—111no—
140C4×#135—111no—
141#2229—112no—
142#2228—112no—
143#2227—111no—
144#2226—111no—
145#2225—111no—
146#2224—111no—
147#2158—112no—
148C2×C4⋊C16D1111yescharacteristic, complemented
149#2138—112no—
150C23×C11C2×D811yescharacteristic
151C22×D11—41no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11C22⋊Q812yes—
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11#13712yes—
161C2×C4×C11C22×D411yescharacteristic
162C22⋊D11—44no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168D44—22no—
169D44—41no—
170C4×D11—44no—
171C4×D11—82no—
172C4×D11—82no—
173Dic22—22no—
174Dic22—41no—
175Dic22—82no—
176Dic22—82no—
177C8×C11—21no—
178C8×C11—21no—
179C8×C11C22⋊Q812yes—
180C8×C11C22×Q811yescharacteristic
181C8×C11C2×#4111yescharacteristic
182C2×#135—111no—
183#533—221no—
184C4×#41—221no—
185C22×C16C2×D1112yes—
186#500—111no—
187#500—111no—
188#499—112no—
189#499—221no—
190#498—221no—
191C4×Q16—111no—
192C4×Q16—111no—
193C4×SD16—221no—
194C4×SD16—221no—
195C4×D8—111no—
196C4×D8—111no—
197#427—112no—
198#427—111no—
199#427—221no—
200#416—221no—
201C2×C4×C8C2×D1111yescharacteristic
202#367—112no—
203#367—112no—
204#366—112no—
205#366—112no—
206C4⋊C16C2×D1111yescharacteristic
207C4⋊C16C2×D1111yescharacteristic
208C4⋊C16C2×D1112yes—
209#358—112no—
210#358—112no—
211#357—112no—
212#357—112no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11#47412yes—
216C22×C11C22×D811yescharacteristic
217C2×D11—42no—
218C2×D11—81no—
219C2×D11—81no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11#47412yes—
224C4×C11#50812yes—
225C4×C11C2×C22⋊Q811yescharacteristic
226C4×C11C2×#13711yescharacteristic
227Dic11—42no—
228Dic11—82no—
229Dic11—81no—
230Dic11—82no—
231Dic11—81no—
232C2×#41—221no—
233#135—114no—
234#135—222no—
235C2×Q16—111no—
236C2×SD16—221no—
237C2×D8—111no—
238C22×C8D4411yescharacteristic
239C22×C8C22×D1111yescharacteristic
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242#125—222no—
243C22⋊Q8—441no—
244C22⋊Q8—441no—
245C4×Q8—221no—
246C4×Q8—221no—
247C4×Q8—441no—
248C4×Q8—441no—
249C4×D4—221no—
250C4×D4—221no—
251C4×D4—441no—
252C4×D4—441no—
253#117—221no—
254#117—222no—
255#117—441no—
256C2×C42—441no—
257C2×C42D4411yescharacteristic
258C2×C16—24no—
259C2×C16C22×D1112yes—
260C2×C16C22×D1112yes—
261#107—112no—
262#107—112no—
263#107—111no—
264#107—111no—
265#107—221no—
266#107—221no—
267#106—221no—
268#106—222no—
269#106—222no—
270#103—221no—
271#103—221no—
272#102—221no—
273#102—221no—
274C4×C8D4411yescharacteristic
275C4×C8D4411yescharacteristic
276C4×C8C22×D1111yescharacteristic
277C4×C8C22×D1111yescharacteristic
278C2×C11—22no—
279C2×C11C2×#47411yescharacteristic
280C2×C11C2×#50811yescharacteristic
281C2×C11#341411yescharacteristic
282D11—82no—
283#41—224no—
284#41—442no—
285C2×Q8—221no—
286C2×Q8—441no—
287C2×Q8—441no—
288C2×D4—221no—
289C2×D4—441no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4D8811yescharacteristic
294C22×C4D8811yescharacteristic
295C22×C4C2×D4411yescharacteristic
296Q16—112no—
297Q16—221no—
298SD16—224no—
299D8—112no—
300D8—221no—
301C2×C8—22no—
302C2×C8C2×D4411yescharacteristic
303C2×C8C2×D4411yescharacteristic
304C2×C8C2×D4411yescharacteristic
305C2×C8#434112yes—
306C2×C8Q8×D1112yes—
307C2×C8C23×D1111yescharacteristic
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—222no—
311C4⋊C4—222no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—442no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C42—441no—
323C42—441no—
324C42—441no—
325C42—442no—
326C42D8811yescharacteristic
327C42D8811yescharacteristic
328C42C2×D4411yescharacteristic
329C42C2×D4411yescharacteristic
330C16—22no—
331C16—22no—
332C11#3362611yescharacteristic, complemented, Sylow
333C23—441no—
334C23C2×D8811yescharacteristic
335Q8—222no—
336Q8—441no—
337Q8—882no—
338Q8—882no—
339D4—222no—
340D4—444no—
341D4—441no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—441no—
345C2×C4—444no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—882no—
351C2×C4—882no—
352C2×C4#6695012yes—
353C2×C4C2×D8811yescharacteristic
354C2×C4C2×D8811yescharacteristic
355C2×C4C2×D8811yescharacteristic
356C2×C4C2×D8811yescharacteristic
357C2×C4C2×D8811yescharacteristic
358C2×C4#6696212yes—
359C2×C4C22×D4411yescharacteristic
360C8—21no—
361C8—21no—
362C8#6695012yes—
363C8C2×#434111yescharacteristic
364C8C2×Q8×D1111yescharacteristic
365C22—21no—
366C22—21no—
367C22—442no—
368C22—881no—
369C22—881no—
370C22#1062245912yes—
371C22C22×D8811yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—442no—
376C4—881no—
377C4—882no—
378C4—881no—
379C4—882no—
380C4#1062245912yes—
381C4#1062251712yes—
382C4C2×#6695011yescharacteristic
383C4C2×#6696211yescharacteristic
384C2—22no—
385C2—882no—
386C2C2×#1062245911yescharacteristic
387C2C2×#1062251711yescharacteristic
388C2#1308175211yescharacteristic
subgroupG/H
centerC2×C4C2×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×C4⋊C16C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenterC2×C4⋊C16D11
hypocenterC11#33626
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
1. #13079130C2semidirect
3. #13070781C2semidirect
4. #13070774C2semidirect
5. #13070769C2semidirect
6. #13070764C2semidirect
7. #13070759C2semidirect
8. #13070754C2semidirect
9. #13070400C2semidirect
11. C2×C11×C4⋊C16C2semidirect
55. #66957Q8semidirect
148. C2×C4⋊C16D11semidirect
332. C11#33626semidirect

Maximal subgroups

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

subgroupindex
#130791302
C4×#669572
#130707812
#130707742
#130707692
#130707642
#130707592
#130707542
#130704002
#130703242
C2×C11×C4⋊C162
#3362611