Finite Group Databasebeta

← #14736933

Subgroups — #14736933

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 426 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#13068179C214yesmaximal, complemented
5#13068055C214yesmaximal, complemented
6#13067362C211yesmaximal, characteristic, complemented
7#13067301C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C11×#3206C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67001—21no—
13C2×#66927C2211yescharacteristic
14C11×#492—21no—
15C11×#487—21no—
16C11×#461C2214yescomplemented
17C11×#448—22no—
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#10622185C2214yescomplemented
38#10622123C2214yes—
39#10622118C2212yescomplemented
40#10622117C2212yescomplemented
41C2×C11×#41—21no—
42C22×Q8×C11—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44—21no—
46C2×C11×SD16—24no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8D411yescharacteristic
51C11×C4⋊Q8C2312yes—
52C11×#127D411yescharacteristic
53C11×#124—21no—
54C11×#121—21no—
55C11×#121D412yes—
56C4×D4×C11—21no—
57C4×D4×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61#67001—44no—
62C2×#4323—24no—
63C2×#4318—21no—
64C2×#4318—22no—
65C22×C11⋊C8—22no—
66C22×C11⋊C8D411yescharacteristic
67C22×C11⋊C8D411yescharacteristic
68#66927—21no—
69#66927—21no—
70#66927—21no—
71#66927C2312yes—
72C11×C4⋊C8C2312yes—
73C11×#103—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#19198—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—
119C11×SD16—84no—
120C2×C8×C11—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4C2×D412yes—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11C2411yescharacteristic
133#4323—84no—
134#4318—44no—
135#4318—42no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—44no—
141C2×C11⋊C8C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144C2×C11⋊C8C2×D411yescharacteristic
145#3206D1111yescharacteristic, complemented
146#3205—111no—
147C2×#486—111no—
148#2931—111no—
149#1701—114no—
150#1681—114no—
151#1564—111no—
152#1549—111no—
153#1545—111no—
154C23×C11—22no—
155C23×C11#12111yescharacteristic
156C22×D11—42no—
157C22×D11—82no—
158C22×D11—82no—
159C22×D11—82no—
160Q8×C11—42no—
161Q8×C11—44no—
162Q8×C11—82no—
163D4×C11—24no—
164D4×C11—44no—
165D4×C11—42no—
166D4×C11—42no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—82no—
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#13512yes—
178C2×C4×C11AGL(1,ℤ/8)12yes—
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182D44—42no—
183D44—42no—
184D44—44no—
185D44—82no—
186D44—82no—
187D44—82no—
188D44—82no—
189C8×C11—42no—
190C11⋊C8—21no—
191C11⋊C8—21no—
192C11⋊C8—21no—
193C11⋊C8—21no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C2×#131—221no—
197#532C2×D1111yescharacteristic
198C2×C4⋊Q8C2×D1111yescharacteristic
199C2×#127—111no—
200#493—221no—
201#492—21no—
202#487—21no—
203#486—112no—
204#486—112no—
205#486—221no—
206#486—221no—
207#486—221no—
208#461C2×D1114yescomplemented
209#459—114no—
210#448—22no—
211#447—222no—
212#436—112no—
213#436—221no—
214C8×D4—112no—
215C8×D4—221no—
216#431—111no—
217#431C2×D1111yescharacteristic
218#423—111no—
219C2×#102—221no—
220C2×#102—221no—
221#408—221no—
222C2×C4×C8—111no—
223#335—112no—
224#334—112no—
225#332—114no—
226#331—114no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11#46312yes—
233C22×C11C2×#12111yescharacteristic
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—164no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—42no—
241C4×C11—82no—
242C4×C11#46312yes—
243C4×C11#47112yes—
244C4×C11C2×#13511yescharacteristic
245C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C11#57612yes—
247C2×#41—21no—
248C22×Q8—21no—
249C22×D4—221no—
250C22×D4—221no—
251C22×D4—221no—
252C2×SD16—24no—
253C2×D8—224no—
254#131—444no—
255C2×M16—222no—
256C2×M16—221no—
257C22×C8—111no—
258C22×C8—111no—
259C22×C8—222no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8C22⋊D1111yescharacteristic
264C4⋊Q8C22×D1112yes—
265#127—112no—
266#127—221no—
267#127—221no—
268#127—221no—
269#127C22⋊D1111yescharacteristic
270#124—21no—
271#121—21no—
272#121C22⋊D1112yes—
273C4×D4—21no—
274C4×D4C22×D1112yes—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C42C22×D1111yescharacteristic
278C4⋊C8—112no—
279C4⋊C8—112no—
280C4⋊C8—221no—
281C4⋊C8C22×D1112yes—
282#103—24no—
283#102—222no—
284#102—222no—
285#102—222no—
286#102—222no—
287#102—224no—
288C22⋊C8—21no—
289C22⋊C8—222no—
290C22⋊C8—222no—
291C22⋊C8—221no—
292C4×C8—21no—
293C4×C8—111no—
294C4×C8—111no—
295C4×C8—111no—
296C4×C8—111no—
297C4×C8—221no—
298C2×C11—22no—
299C2×C11—82no—
300C2×C11C2×#46311yescharacteristic
301C2×C11#305811yescharacteristic
302C2×C11C2×#47111yescharacteristic
303D11—162no—
304C24—441no—
305#41—42no—
306#41—42no—
307C2×Q8—21no—
308C2×Q8—22no—
309C2×Q8—41no—
310C2×Q8—82no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—222no—
315C2×D4—222no—
316C2×D4—222no—
317C2×D4—442no—
318C2×D4—442no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—441no—
322C2×D4—882no—
323C2×D4—882no—
324C2×D4C2×C22⋊D1112yes—
325C22×C4—22no—
326C22×C4—41no—
327C22×C4D4×D1111yescharacteristic
328C22×C4#434111yescharacteristic
329C22×C4C2×C22⋊D1111yescharacteristic
330SD16—84no—
331D8—884no—
332M16—444no—
333M16—442no—
334C2×C8—22no—
335C2×C8—111no—
336C2×C8—111no—
337C2×C8—111no—
338C2×C8—111no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—444no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4C2×C22⋊D1112yes—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C42D4×D1111yescharacteristic
353C42#434111yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C42C23×D1111yescharacteristic
356C11#1919811yescharacteristic, complemented, Sylow
357C23—22no—
358C23—442no—
359C23—882no—
360C23—882no—
361C23—882no—
362C23#6699211yescharacteristic
363Q8—42no—
364Q8—44no—
365Q8—82no—
366D4—24no—
367D4—44no—
368D4—42no—
369D4—42no—
370D4—442no—
371D4—442no—
372D4—444no—
373D4—882no—
374D4—882no—
375D4—882no—
376D4—882no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—82no—
384C2×C4#6696712yes—
385C2×C4#6696912yes—
386C2×C4#6699211yescharacteristic
387C2×C4#6699211yescharacteristic
388C2×C4#6699211yescharacteristic
389C2×C4C2×D4×D1111yescharacteristic
390C2×C4C2×#434111yescharacteristic
391C2×C4C22×C22⋊D1111yescharacteristic
392C8—42no—
393C8—221no—
394C8—221no—
395C8—221no—
396C8—221no—
397C8—442no—
398C8—442no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—882no—
405C22—882no—
406C22—882no—
407C22—1764no—
408C22#1062277812yes—
409C22C2×#6699211yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—82no—
414C4#1062277812yes—
415C4#1062281612yes—
416C4C2×#6696711yescharacteristic
417C4C2×#6696911yescharacteristic
418C4#1062336612yes—
419C2—22no—
420C2—82no—
421C2—1762no—
422C2C2×#1062277811yescharacteristic
423C2#1307826111yescharacteristic
424C2C2×#1062281611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3206C2
socleC22×C11C2×#121
prime radical#13079531C2
hypercenter#3206D11
hypocenterC11#19198
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
2. C2×#10622701C2semidirect
3. #13077328C2semidirect
4. #13068179C2semidirect
5. #13068055C2semidirect
6. #13067362C2semidirect
7. #13067301C2semidirect
8. #13067283C2semidirect
9. C11×#3206C2semidirect
16. C11×#461C22semidirect
29. #10622625C22semidirect
31. D4×C11⋊C8C22semidirect
37. #10622185C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
145. #3206D11semidirect
208. #461C2×D11semidirect
356. C11#19198semidirect

Maximal subgroups

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

subgroupindex
#130795312
C2×#106227012
#130773282
#130681792
#130680552
#130673622
#130673012
#130672832
C11×#32062
#1919811