Finite Group Databasebeta

← #14736915

Subgroups — #14736915

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079531C211yesmaximal, characteristic
2C2×#10622701C211yesmaximal, characteristic, complemented
3#13077328C211yesmaximal, characteristic, complemented
4#13068151C214yesmaximal, complemented
5#13068027C214yesmaximal, complemented
6#13067362C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C11×#3227C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67001—21no—
13C2×#66927C2211yescharacteristic
14C11×#498—21no—
15C11×#486—21no—
16C11×#481—22no—
17C11×#476C2214yescomplemented
18C11×#431C2211yescharacteristic
19#10622847—21no—
20#10622701—21no—
21#10622701—21no—
22#10622701—21no—
23#10622701C2212yes—
24#10622701C2212yes—
25#10622686—21no—
26#10622649—22no—
27#10622628C2214yes—
28#10622625—21no—
29#10622625C2212yescomplemented
30D4×C11⋊C8—21no—
31D4×C11⋊C8C2212yescomplemented
32C2×#66873—21no—
33C2×#66873—21no—
34#10622538C2211yescharacteristic
35#10622537C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622184C2214yescomplemented
38#10622123C2214yes—
39#10622118C2212yescomplemented
40#10622117C2212yescomplemented
41C2×C11×#41—21no—
42C22×Q8×C11—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8D411yescharacteristic
50C11×C4⋊Q8C2312yes—
51C11×#127D411yescharacteristic
52C11×#124—21no—
53C11×#121—21no—
54C11×#121D412yes—
55C4×D4×C11—21no—
56C4×D4×C11C2312yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60#67001—44no—
61C2×#4323—24no—
62C2×#4318—21no—
63C2×#4318—22no—
64C22×C11⋊C8—22no—
65C22×C11⋊C8D411yescharacteristic
66C22×C11⋊C8D411yescharacteristic
67#66927—21no—
68#66927—21no—
69#66927—21no—
70#66927C2312yes—
71C11×#106—24no—
72C11×C4⋊C8C2312yes—
73C11×#102—24no—
74C11×C22⋊C8—21no—
75C4×C8×C11—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)—22no—
79#66873—24no—
80#66873—22no—
81#66873—22no—
82#66873—22no—
83#66873—22no—
84C4⋊(C11⋊C8)—21no—
85C4⋊(C11⋊C8)C2312yes—
86C4⋊(C11⋊C8)C2312yes—
87C4×C11⋊C8—21no—
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92#19196—111nomaximal, Sylow
93C23×D11—41no—
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—41no—
99C2×Q8×C11—82no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11C2×D412yes—
104C22×C4×C11—22no—
105C22×C4×C11—41no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—41no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—42no—
116C2×D44—42no—
117C2×D44—82no—
118C2×D44—82no—
119C2×C8×C11—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4C2×D412yes—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132#4323—84no—
133#4318—44no—
134#4318—42no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—44no—
140C2×C11⋊C8C2×D411yescharacteristic
141C2×C11⋊C8C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144#3227D1111yescharacteristic, complemented
145#3205—111no—
146C2×#486—111no—
147#2931—111no—
148#1697—114no—
149#1677—114no—
150#1564—111no—
151#1548—111no—
152#1545—111no—
153C23×C11—22no—
154C23×C11#12111yescharacteristic
155C22×D11—42no—
156C22×D11—82no—
157C22×D11—82no—
158C22×D11—82no—
159Q8×C11—42no—
160Q8×C11—82no—
161Q8×C11—82no—
162D4×C11—24no—
163D4×C11—44no—
164D4×C11—42no—
165D4×C11—42no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#13512yes—
177C2×C4×C11AGL(1,ℤ/8)12yes—
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181D44—42no—
182D44—42no—
183D44—44no—
184D44—82no—
185D44—82no—
186D44—82no—
187D44—82no—
188C8×C11—42no—
189C11⋊C8—21no—
190C11⋊C8—21no—
191C11⋊C8—21no—
192C11⋊C8—21no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195C2×#131—221no—
196#532C2×D1111yescharacteristic
197C2×C4⋊Q8C2×D1111yescharacteristic
198C2×#127—111no—
199#498—21no—
200#493—221no—
201#486—21no—
202#486—112no—
203#486—112no—
204#486—221no—
205#486—221no—
206#486—221no—
207#481—22no—
208#476C2×D1114yescomplemented
209#459—114no—
210#447—222no—
211#436—112no—
212#436—221no—
213C8×D4—112no—
214C8×D4—221no—
215#431—111no—
216#431C2×D1111yescharacteristic
217#423—111no—
218C2×#102—221no—
219C2×#102—221no—
220#408—221no—
221C2×C4×C8—111no—
222#335—112no—
223#334—112no—
224#333—114no—
225#331—114no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11#46312yes—
232C22×C11C2×#12111yescharacteristic
233C2×D11—82no—
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—164no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—42no—
240C4×C11—82no—
241C4×C11#46312yes—
242C4×C11#47212yes—
243C4×C11C2×#13511yescharacteristic
244C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C11#57712yes—
246C2×#41—21no—
247C22×Q8—21no—
248C22×D4—221no—
249C22×D4—221no—
250C22×D4—221no—
251C2×D8—224no—
252#131—444no—
253C2×M16—222no—
254C2×M16—221no—
255C22×C8—111no—
256C22×C8—111no—
257C22×C8—222no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8C22⋊D1111yescharacteristic
262C4⋊Q8C22×D1112yes—
263#127—112no—
264#127—221no—
265#127—221no—
266#127—221no—
267#127C22⋊D1111yescharacteristic
268#124—21no—
269#121—21no—
270#121C22⋊D1112yes—
271C4×D4—21no—
272C4×D4C22×D1112yes—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C42C22×D1111yescharacteristic
276#106—24no—
277C4⋊C8—112no—
278C4⋊C8—112no—
279C4⋊C8—221no—
280C4⋊C8C22×D1112yes—
281#102—24no—
282#102—222no—
283#102—222no—
284#102—222no—
285#102—222no—
286#102—224no—
287C22⋊C8—21no—
288C22⋊C8—222no—
289C22⋊C8—222no—
290C22⋊C8—221no—
291C4×C8—21no—
292C4×C8—111no—
293C4×C8—111no—
294C4×C8—111no—
295C4×C8—111no—
296C4×C8—221no—
297C2×C11—22no—
298C2×C11—82no—
299C2×C11C2×#46311yescharacteristic
300C2×C11#305711yescharacteristic
301C2×C11C2×#47211yescharacteristic
302D11—162no—
303C24—441no—
304#41—42no—
305#41—42no—
306C2×Q8—21no—
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—82no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—222no—
314C2×D4—222no—
315C2×D4—222no—
316C2×D4—442no—
317C2×D4—442no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—882no—
322C2×D4—882no—
323C2×D4C2×C22⋊D1112yes—
324C22×C4—22no—
325C22×C4—41no—
326C22×C4D4×D1111yescharacteristic
327C22×C4#434111yescharacteristic
328C22×C4C2×C22⋊D1111yescharacteristic
329D8—884no—
330M16—444no—
331M16—442no—
332C2×C8—22no—
333C2×C8—111no—
334C2×C8—111no—
335C2×C8—111no—
336C2×C8—111no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—444no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4C2×C22⋊D1112yes—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C42D4×D1111yescharacteristic
351C42#434111yescharacteristic
352C42C2×C22⋊D1111yescharacteristic
353C42C23×D1111yescharacteristic
354C11#1919611yescharacteristic, complemented, Sylow
355C23—22no—
356C23—442no—
357C23—882no—
358C23—882no—
359C23—882no—
360C23#6699211yescharacteristic
361Q8—42no—
362Q8—82no—
363Q8—82no—
364D4—24no—
365D4—44no—
366D4—42no—
367D4—42no—
368D4—442no—
369D4—442no—
370D4—444no—
371D4—882no—
372D4—882no—
373D4—882no—
374D4—882no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—82no—
382C2×C4#6696712yes—
383C2×C4#6696912yes—
384C2×C4#6699211yescharacteristic
385C2×C4#6699211yescharacteristic
386C2×C4#6699211yescharacteristic
387C2×C4C2×D4×D1111yescharacteristic
388C2×C4C2×#434111yescharacteristic
389C2×C4C22×C22⋊D1111yescharacteristic
390C8—42no—
391C8—221no—
392C8—221no—
393C8—221no—
394C8—221no—
395C8—442no—
396C8—442no—
397C22—21no—
398C22—21no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—882no—
403C22—882no—
404C22—882no—
405C22—1764no—
406C22#1062277812yes—
407C22C2×#6699211yescharacteristic
408C4—21no—
409C4—21no—
410C4—42no—
411C4—82no—
412C4#1062277812yes—
413C4#1062281212yes—
414C4C2×#6696711yescharacteristic
415C4C2×#6696911yescharacteristic
416C4#1062336812yes—
417C2—22no—
418C2—82no—
419C2—1762no—
420C2C2×#1062277811yescharacteristic
421C2#1307825711yescharacteristic
422C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3227C2
socleC22×C11C2×#121
prime radical#13079531C2
hypercenter#3227D11
hypocenterC11#19196
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. C2×#10622701C2semidirect
3. #13077328C2semidirect
4. #13068151C2semidirect
5. #13068027C2semidirect
6. #13067362C2semidirect
7. #13067297C2semidirect
8. #13067283C2semidirect
9. C11×#3227C2semidirect
17. C11×#476C22semidirect
29. #10622625C22semidirect
31. D4×C11⋊C8C22semidirect
37. #10622184C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
144. #3227D11semidirect
208. #476C2×D11semidirect
354. C11#19196semidirect

Maximal subgroups

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

subgroupindex
#130795312
C2×#106227012
#130773282
#130681512
#130680272
#130673622
#130672972
#130672832
C11×#32272
#1919611