Finite Group Databasebeta

← #14756969

Subgroups — #14756969

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4326C211yesmaximal, characteristic
2#13070979C211yesmaximal, characteristic
3#13069254C212yesmaximal
4#13069184C212yesmaximal
5#13068960C212yesmaximal
6#13068869C212yesmaximal
7C4×#66871C211yesmaximal, characteristic
8#13068449C211yesmaximal, characteristic
9#13068446C211yesmaximal, characteristic
10#13068368C211yesmaximal, characteristic
11C11×#2320C211yesmaximal, characteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4326C2211yescharacteristic
14C2×C4×Dic22C2212yes—
15C2×C4×Dic22C2211yescharacteristic
16C11×#391C2212yes—
17C11×#389C2212yes—
18C11×#387—22no—
19C11×#383—21no—
20C11×#382—21no—
21C4×C11×C4⋊C4C2211yescharacteristic
22C11×#376C2211yescharacteristic
23C2×#66899C2212yes—
24C2×#66899C2211yescharacteristic
25C4×#4326C418yescomplemented
26C2×#66874C2212yes—
27C2×#66874C2211yescharacteristic
28C2×#66871C2212yes—
29C2×#66871C2211yescharacteristic
30C4×C4⋊Dic11C2212yes—
31C4×C4⋊Dic11C2211yescharacteristic
32C2×#66867C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622262—21no—
35#10622262—22no—
36#10622261—21no—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2212yes—
41#10622162C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×Dic22C2311yescharacteristic
44C4×Q8×C11—22no—
45C4×Q8×C11C2×C414yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×#4326—24no—
55C2×#4326C2×C414yes—
56C2×C4⋊Dic11C2311yescharacteristic
57C2×C4⋊Dic11C2312yes—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—21no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—21no—
64C22×C11⋊C8C2312yes—
65C22×C11⋊C8C2311yescharacteristic
66C22×C11⋊C8C2311yescharacteristic
67C4×Dic22—24no—
68C4×Dic22—22no—
69C4×Dic22—24no—
70C4×Dic22C2×C414yes—
71C11×#95—21no—
72C11×#95—22no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95D411yescharacteristic
76C11×#95D411yescharacteristic
77C11×#95D412yes—
78#66899—24no—
79#66899C2×C414yes—
80C11⋊#95—22no—
81C11⋊#95—21no—
82#66874—24no—
83#66874C2×C414yes—
84#66871—24no—
85#66871C2×C414yes—
86#66867—22no—
87C4×C11⋊C8C2×C414yes—
88#21135—111nomaximal, Sylow
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11C22×C412yes—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C2×Dic22—21no—
105C2×Dic22—22no—
106C2×Dic22C22×C412yes—
107C2×Dic22#4114yes—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—82no—
113C11×C4⋊C4C22×C412yes—
114C42×C11—24no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—81no—
118C42×C11C22×C412yes—
119C42×C11#4112yes—
120#4326—28no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11C22×C412yes—
124C4⋊Dic11#4114yes—
125Dic11⋊C4—28no—
126Dic11⋊C4—24no—
127C4×Dic11—28no—
128C4×Dic11—24no—
129C4×Dic11—81no—
130C4×Dic11—82no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8C22×C412yes—
137C2×C11⋊C8C22×C412yes—
138C2×C4×Q16—111no—
139#2320D1111yescharacteristic
140#2276—111no—
141#1928—112no—
142#1918—112no—
143#1878—112no—
144#1863—112no—
145C4×#107—111no—
146#1763—111no—
147#1763—111no—
148#1746—111no—
149C23×C11C22×D411yescharacteristic
150Q8×C11—22no—
151Q8×C11—22no—
152Q8×C11—42no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11C4×D412yes—
171C2×C4×C11C4×D412yes—
172C2×C4×C11C23×C411yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C2×C4×C11C2×#4112yes—
175C2×C4×C11C2×#4112yes—
176C2×Dic11—22no—
177C2×Dic11—24no—
178C2×Dic11—22no—
179C2×Dic11—24no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184Dic22—22no—
185Dic22—24no—
186Dic22#11714yes—
187C11⋊C8—22no—
188C11⋊C8—22no—
189C11⋊C8—42no—
190C22×Q16—111no—
191C2×C4×Q8—111no—
192C2×C4×Q8—112no—
193C2×C4×Q8C2×D1111yescharacteristic
194C4×Q16—118no—
195C2×#107—111no—
196C2×#107—112no—
197C2×#103—111no—
198C2×#103—111no—
199C2×#103—112no—
200C2×#103—112no—
201C2×#97—111no—
202C2×C4×C8—111no—
203#391C2×D1112yes—
204#389C2×D1112yes—
205#387—22no—
206#383—21no—
207#382—21no—
208C4×C4⋊C4—112no—
209C4×C4⋊C4—111no—
210C4×C4⋊C4—221no—
211C4×C4⋊C4—222no—
212C4×C4⋊C4C2×D1111yescharacteristic
213#376—221no—
214#376C2×D1111yescharacteristic
215#340—112no—
216#340—112no—
217#340—112no—
218#336—112no—
219#336—112no—
220C22×C11C2×C4×D411yescharacteristic
221C22×C11#52512yes—
222C22×C11#57611yescharacteristic
223C22×C11#57812yes—
224C22×C11#57811yescharacteristic
225C4×C11—22no—
226C4×C11—22no—
227C4×C11—42no—
228C4×C11—42no—
229C4×C11—42no—
230C4×C11—42no—
231C4×C11—82no—
232C4×C11C2×#11711yescharacteristic
233C4×C11C4×#4111yescharacteristic
234C4×C11#52912yes—
235Dic11—24no—
236Dic11—44no—
237Dic11—42no—
238C22×Q8—111no—
239C22×Q8C22×D1111yescharacteristic
240C2×Q16—114no—
241C2×Q16—224no—
242C22×C8—111no—
243C22×C8—111no—
244C22×C8—112no—
245C4×Q8—22no—
246C4×Q8—114no—
247C4×Q8—224no—
248C4×Q8—224no—
249C4×Q8—222no—
250C4×Q8C4×D1114yes—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—222no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4C22×D1112yes—
258C2×C4⋊C4C22×D1111yescharacteristic
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—222no—
262C2×C42—221no—
263C2×C42—222no—
264C2×C42—221no—
265C2×C42C22×D1112yes—
266C2×C42C22×D1111yescharacteristic
267#107—114no—
268#107—224no—
269#103—114no—
270#103—114no—
271#103—224no—
272#103—224no—
273#97—222no—
274C4×C8—114no—
275#95—21no—
276#95—22no—
277#95—22no—
278#95—22no—
279#95—222no—
280#95—221no—
281#95C22⋊D1111yescharacteristic
282#95C22⋊D1111yescharacteristic
283#95C22⋊D1112yes—
284C2×C11#229011yescharacteristic
285C2×C11#295011yescharacteristic
286C2×C11#295111yescharacteristic
287C2×C11#312412yes—
288C2×C11#312712yes—
289C2×Q8—21no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—112no—
293C2×Q8—114no—
294C2×Q8—221no—
295C2×Q8—222no—
296C2×Q8C2×C4×D1112yes—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—222no—
303C22×C4C2×C22⋊D1112yes—
304C22×C4C2×C22⋊D1112yes—
305C22×C4C2×C22⋊D1111yescharacteristic
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C23×D1111yescharacteristic
308Q16—228no—
309C2×C8—112no—
310C2×C8—112no—
311C2×C8—222no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C4⋊C4—24no—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—82no—
321C4⋊C4—112no—
322C4⋊C4—114no—
323C4⋊C4—228no—
324C4⋊C4—224no—
325C4⋊C4—221no—
326C4⋊C4—222no—
327C4⋊C4C2×C4×D1112yes—
328C42—24no—
329C42—22no—
330C42—22no—
331C42—81no—
332C42—228no—
333C42—224no—
334C42—881no—
335C42—882no—
336C42C2×C4×D1112yes—
337C42#433912yes—
338C11#2113511yescharacteristic, complemented, Sylow
339C23C22×C22⋊D1111yescharacteristic
340Q8—22no—
341Q8—22no—
342Q8—42no—
343Q8—114no—
344Q8—222no—
345Q8—224no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—222no—
364C2×C4—224no—
365C2×C4—222no—
366C2×C4—224no—
367C2×C4—442no—
368C2×C4—441no—
369C2×C4—442no—
370C2×C4—441no—
371C2×C4C4×C22⋊D1112yes—
372C2×C4C4×C22⋊D1112yes—
373C2×C4C22×C4×D1111yescharacteristic
374C2×C4C2×#433911yescharacteristic
375C2×C4#41×D1112yes—
376C2×C4#41×D1112yes—
377C8—222no—
378C8—222no—
379C8—442no—
380C22C2×C4×C22⋊D1111yescharacteristic
381C22#1062335912yes—
382C22#1062336611yescharacteristic
383C22#1062336912yes—
384C22#1062336911yescharacteristic
385C4—22no—
386C4—22no—
387C4—42no—
388C4—42no—
389C4—42no—
390C4—42no—
391C4—82no—
392C4—224no—
393C4—444no—
394C4—442no—
395C4D11×#11711yescharacteristic
396C4#1062305311yescharacteristic
397C4#1062305912yes—
398C2#1307105311yescharacteristic
399C2#1307748211yescharacteristic
400C2#1307748911yescharacteristic
401C2#1307887212yes—
402C2#1307891112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2320C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#2320D11
hypocenterC11#21135
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
25. C4×#4326C4semidirect
338. C11#21135semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43262
#130709792
#130692542
#130691842
#130689602
#130688692
C4×#668712
#130684492
#130684462
#130683682
C11×#23202
#2113511