Finite Group Databasebeta

← #14757197

Subgroups — #14757197

Order 2816.

890 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622506C211yesmaximal, characteristic
2#13077204C211yesmaximal, characteristic
3D11×#424C212yesmaximal
4C2×#10622302C211yesmaximal, characteristic
5#13069370C211yesmaximal, characteristic, complemented
6#13069368C212yesmaximal, complemented
7#13069367C211yesmaximal, characteristic, complemented
8#13069364C211yesmaximal, characteristic, complemented
9#13069361C212yesmaximal, complemented
10#13068324C212yesmaximal
11C11×#1945C211yesmaximal, characteristic, complemented
12C2×M16×D11C2212yes—
13C22×#4313C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15D11×#117C2212yes—
16C2×#66925C2211yescharacteristic
17C2×C11×#108C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C11×#424C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21C2×#66886C2212yes—
22#10622732C2212yes—
23C2×#66883C2211yescharacteristic
24#10622719C2211yescharacteristic
25#10622715C2212yes—
26C2×#66879C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622612C2212yes—
29#10622611C2212yes—
30C2×#66867C2211yescharacteristic
31#10622506—24no—
32#10622494C414yescomplemented
33#10622474C414yescomplemented
34#10622452—24no—
35D11×C4⋊C8—24no—
36#10622302—24no—
37C11×#339C2212yes—
38#10622193C2212yes—
39#10622170C2212yes—
40#10622161C2212yes—
41C22×C4×D11C2311yescharacteristic
42C2×C11×M16C2312yes—
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C11×#117C2312yes—
46C2×C42×C11C2311yescharacteristic
47C2×(C2×D11)⋊C4—21no—
48#66979C2312yes—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11C2311yescharacteristic
51C2×#4318C2312yes—
52C22×C11⋊C8C2311yescharacteristic
53C22×C11⋊C8C2311yescharacteristic
54M16×D11—24no—
55M16×D11—24no—
56C2×#4313—22no—
57C2×#4313C2×C412yes—
58C2×#4313C2×C412yes—
59C2×#4313D414yes—
60C2×#4313Q814yes—
61C2×C8×D11—22no—
62C2×C8×D11—22no—
63C2×C8×D11—22no—
64C2×C8×D11D414yes—
65#66945C2×C414yes—
66C4⋊C4×D11C2×C414yes—
67C22⋊C4×D11—22no—
68#66930—22no—
69#66925—22no—
70#66925—22no—
71#66925Q814yes—
72C42×D11—22no—
73C11×#108—22no—
74C11×#107C2×C412yes—
75C11×#106C2×C412yes—
76C11×C4⋊C8—24no—
77C4×C8×C11—22no—
78#66886—24no—
79#66883—22no—
80#66882C2×C412yes—
81#66881C2×C412yes—
82#66879—22no—
83Dic11⋊C8—24no—
84Dic11⋊C8—24no—
85C8×Dic11—22no—
86#66872C2×C414yes—
87#66871C2×C414yes—
88C4⋊(C11⋊C8)—24no—
89#66867—22no—
90#21164—111nomaximal, Sylow
91C23×D11#4111yescharacteristic
92C22×C4×C11—21no—
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—21no—
95C22×Dic11#4111yescharacteristic
96C2×C4×D11—24no—
97C2×C4×D11C22×C412yes—
98C2×C4×D11C2×D412yes—
99C2×C4×D11C2×D412yes—
100C2×C4×D11C2×Q812yes—
101C2×C4×D11C2×Q812yes—
102C2×C4×D11#4112yes—
103C11×M16—22no—
104C11×M16—22no—
105C2×C8×C11—21no—
106C2×C8×C11—22no—
107C2×C8×C11—21no—
108C2×C8×C11C22×C411yescharacteristic
109C2×C8×C11C22×C411yescharacteristic
110C2×C8×C11C2×D412yes—
111C2×C8×C11C2×D412yes—
112C2×C8×C11C2×Q812yes—
113C11×C4⋊C4C22×C414yes—
114C11×C22⋊C4—22no—
115C42×C11—21no—
116C42×C11—22no—
117C42×C11C2×Q812yes—
118C22⋊Dic11—22no—
119(C2×D11)⋊C4—24no—
120(C2×D11)⋊C4—24no—
121C4⋊Dic11C22×C414yes—
122Dic11⋊C4—24no—
123Dic11⋊C4—24no—
124C4×Dic11—24no—
125C4×Dic11—21no—
126C4×Dic11—22no—
127C4×Dic11C2×Q812yes—
128#4318—22no—
129#4318—22no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8C22×C412yes—
134C2×C11⋊C8C2×D412yes—
135C2×C11⋊C8C2×D412yes—
136C2×C11⋊C8C2×Q812yes—
137#4313—44no—
138#4313C4⋊C418yes—
139#4313C4⋊C418yes—
140C8×D11—28no—
141C8×D11—44no—
142C2×#430—111no—
143#2911—111no—
144C2×#424—112no—
145C2×#405—111no—
146#1946—111no—
147#1946—111no—
148#1946—112no—
149#1945—112no—
150#1945—111no—
151#1945D1111yescharacteristic, complemented
152#1733—112no—
153C23×C11C2×#4111yescharacteristic
154C22×D11—42no—
155C22×D11C4×D412yes—
156C22×D11C22⋊Q812yes—
157C22×D11#12512yes—
158C2×C4×C11—24no—
159C2×C4×C11—22no—
160C2×C4×C11—42no—
161C2×C4×C11C23×C411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C22×Q811yescharacteristic
165C2×C4×C11C22×Q811yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×Dic11—24no—
168C2×Dic11—22no—
169C2×Dic11—42no—
170C2×Dic11C4×D412yes—
171C2×Dic11C22⋊Q812yes—
172C2×Dic11#12512yes—
173C4×D11—48no—
174C4×D11C2×C4⋊C414yes—
175C4×D11C4×Q814yes—
176C4×D11#12114yes—
177C4×D11C4⋊Q814yes—
178C8×C11—22no—
179C8×C11—42no—
180C8×C11C2×C4⋊C412yes—
181C8×C11C2×C4⋊C412yes—
182C11⋊C8—22no—
183C11⋊C8—42no—
184C11⋊C8C2×C4⋊C414yes—
185C22×M16—111no—
186C22×M16—112no—
187C23×C8—111no—
188C2×#117—111no—
189C2×#117—112no—
190#430—224no—
191C2×#108—112no—
192C2×#108—111no—
193C2×#108C2×D1111yescharacteristic
194#428—114no—
195#428—114no—
196#427—111no—
197#427—112no—
198#427C2×D1111yescharacteristic
199#424—112no—
200#424—112no—
201#424—112no—
202#424—224no—
203#424C2×D1112yes—
204C2×C4⋊C8—224no—
205#405—224no—
206C2×#97—111no—
207C2×#97—111no—
208C2×C4×C8—111no—
209C2×C4×C8C2×D1111yescharacteristic
210#339—112no—
211#339—112no—
212#339—112no—
213#339C2×D1112yes—
214C22×C11—22no—
215C22×C11C2×C4×D411yescharacteristic
216C22×C11C2×C22⋊Q811yescharacteristic
217C22×C11C2×#12511yescharacteristic
218C2×D11—24no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11#38914yes—
222C4×C11—42no—
223C4×C11—44no—
224C4×C11C22×C4⋊C411yescharacteristic
225C4×C11C2×C4×Q811yescharacteristic
226C4×C11C2×#12111yescharacteristic
227C4×C11C2×C4⋊Q811yescharacteristic
228Dic11—42no—
229Dic11—44no—
230Dic11#38914yes—
231C23×C4—111no—
232C2×M16—112no—
233C2×M16—112no—
234C2×M16—114no—
235C2×M16—114no—
236C2×M16—112no—
237C2×M16—222no—
238C2×M16—224no—
239C2×M16—224no—
240C2×M16C22×D1112yes—
241C22×C8—111no—
242C22×C8—111no—
243C22×C8—114no—
244C22×C8—222no—
245C22×C8—222no—
246C22×C8—222no—
247C22×C8C22×D1111yescharacteristic
248C22×C8C22×D1111yescharacteristic
249#117—114no—
250#117—112no—
251#117—114no—
252#117—222no—
253#117—222no—
254#117—222no—
255#117C22×D1112yes—
256C2×C4⋊C4—114no—
257C2×C4⋊C4—221no—
258C2×C22⋊C4—222no—
259C2×C22⋊C4—221no—
260C2×C42—111no—
261C2×C42—222no—
262C2×C42C22×D1111yescharacteristic
263#108—22no—
264#108—224no—
265#108—222no—
266#107—112no—
267#107—114no—
268#107C4×D1112yes—
269#106—112no—
270#106—114no—
271#106C4×D1112yes—
272C4⋊C8—24no—
273C4⋊C8—224no—
274C4⋊C8—224no—
275C4⋊C8—224no—
276#97—222no—
277#97—222no—
278C4×C8—22no—
279C4×C8—222no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11C2×#38911yescharacteristic
283C2×C11#295512yes—
284D11—24no—
285C24—111no—
286C22×C4—21no—
287C22×C4—111no—
288C22×C4—112no—
289C22×C4—112no—
290C22×C4—112no—
291C22×C4—112no—
292C22×C4—112no—
293C22×C4—112no—
294C22×C4—224no—
295C22×C4—221no—
296C22×C4C23×D1111yescharacteristic
297M16—22no—
298M16—22no—
299M16—118no—
300M16—118no—
301M16—222no—
302M16—222no—
303M16—444no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—112no—
308C2×C8—112no—
309C2×C8—112no—
310C2×C8—112no—
311C2×C8—228no—
312C2×C8—221no—
313C2×C8—221no—
314C2×C8—222no—
315C2×C8—444no—
316C2×C8C2×C4×D1111yescharacteristic
317C2×C8C2×C4×D1111yescharacteristic
318C2×C8D4×D1112yes—
319C2×C8D4×D1112yes—
320C2×C8Q8×D1112yes—
321C4⋊C4—114no—
322C4⋊C4—224no—
323C4⋊C4—224no—
324C4⋊C4C2×C4×D1114yes—
325C22⋊C4—22no—
326C22⋊C4—224no—
327C22⋊C4—224no—
328C22⋊C4—222no—
329C42—21no—
330C42—22no—
331C42—112no—
332C42—224no—
333C42—221no—
334C42—222no—
335C42Q8×D1112yes—
336C11#2116411yescharacteristic, complemented, Sylow
337C23—112no—
338C23—112no—
339C23—112no—
340C23—442no—
341C23#41×D1111yescharacteristic
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—112no—
348C2×C4—114no—
349C2×C4—114no—
350C2×C4—114no—
351C2×C4—114no—
352C2×C4—224no—
353C2×C4—222no—
354C2×C4—448no—
355C2×C4—442no—
356C2×C4C22×C4×D1111yescharacteristic
357C2×C4C2×D4×D1111yescharacteristic
358C2×C4C2×D4×D1111yescharacteristic
359C2×C4C2×Q8×D1111yescharacteristic
360C2×C4C2×Q8×D1111yescharacteristic
361C2×C4#41×D1111yescharacteristic
362C8—22no—
363C8—42no—
364C8—114no—
365C8—222no—
366C8—442no—
367C8C4⋊C4×D1112yes—
368C8C4⋊C4×D1112yes—
369C22—22no—
370C22—114no—
371C22—224no—
372C22—442no—
373C22—442no—
374C22C4×D4×D1111yescharacteristic
375C22D11×C22⋊Q811yescharacteristic
376C22D11×#12511yescharacteristic
377C4—42no—
378C4—44no—
379C4—114no—
380C4—442no—
381C4—444no—
382C4C2×C4⋊C4×D1111yescharacteristic
383C4C4×Q8×D1111yescharacteristic
384C4D11×#12111yescharacteristic
385C4D11×C4⋊Q811yescharacteristic
386C2—21no—
387C2—21no—
388C2—224no—
389C2D11×#38911yescharacteristic
390C2#1307751412yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1945C2
socleC22×C11C2×C4×D4
prime radicalC23×D11#41
cosocleC22×C4×C11C24
hypercenter#1945D11
hypocenterC11#21164
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

Complements

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

NH ≅ G/Ntype
5. #13069370C2semidirect
6. #13069368C2semidirect
7. #13069367C2semidirect
8. #13069364C2semidirect
9. #13069361C2semidirect
11. C11×#1945C2semidirect
32. #10622494C4semidirect
33. #10622474C4semidirect
151. #1945D11semidirect
336. C11#21164semidirect

Maximal subgroups

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

subgroupindex
C2×#106225062
#130772042
D11×#4242
C2×#106223022
#130693702
#130693682
#130693672
#130693642
#130693612
#130683242
C11×#19452
#2116411