Finite Group Databasebeta

← #15620039

Subgroups — #15620039

Order 2816.

1744 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#13082238C211yesmaximal, characteristic
2#13077766C216yesmaximal, complemented
3#13077748C211yesmaximal, characteristic, complemented
4#13077745C213yesmaximal, complemented
5#13077717C213yesmaximal, complemented
6#13077695C212yesmaximal, complemented
7#13077617C216yesmaximal, complemented
8#13077582C213yesmaximal, complemented
9Q8×#4313C212yesmaximal, complemented
10#13077550C213yesmaximal, complemented
11C8×C11×#41C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623362C412yes—
14Q8×D44C411yescharacteristic
15C4×Q8×D11C2212yes—
16#10623101C411yescharacteristic
17#10623088C2216yes—
18#10623082C413yes—
19#10623073C413yes—
20#10623060C416yes—
21C4×#4339C2213yes—
22#10623001C2213yes—
23C8×Q8×C11C2211yescharacteristic
24C8×Q8×C11C2211yescharacteristic
25C8×D4×C11C2213yes—
26C8×D4×C11C2213yes—
27C11×#431C2213yes—
28C2×C4×C8×C11C2213yes—
29#10622724C2216yes—
30#10622724C2216yes—
31#10622715C2216yes—
32#10622714C2216yes—
33Q8×C11⋊C8C2212yes—
34#10622625C2216yes—
35#10622538C2213yes—
36#10622537C2213yes—
37#10622450C2216yes—
38#10622446C2216yes—
39#10622444C2216yes—
40#10622443C2216yes—
41#10622342C22112yes—
42#10622333C22112yes—
43#10622301C2211yescharacteristic
44#10622301C2213yes—
45C4×#4313C2216yes—
46#10622298C2216yes—
47#10622292C2213yes—
48#10622292C2216yes—
49#10622292C2213yes—
50C8×Dic22C2216yes—
51C8×Dic22C2216yes—
52C2×C11×#41C2×C411yescharacteristic
53C2×Q8×D11C2×C412yes—
54C2×#4339C2×C413yes—
55C22×C8×C11C2313yes—
56C22×C8×C11C2313yes—
57C4×Q8×C11C2×C411yescharacteristic
58C4×Q8×C11C2311yescharacteristic
59C4×D4×C11C2×C413yes—
60C4×D4×C11C2313yes—
61C11×#117C2×C413yes—
62C2×C42×C11C2313yes—
63Q8×Dic11C2×C412yes—
64#66991C2×C416yes—
65#66989C2×C416yes—
66C4×C22⋊D11C2×C416yes—
67C4×C22⋊D11C2316yes—
68#66979C2×C413yes—
69#66979C2316yes—
70#66977C2×C416yes—
71#66977C2×C416yes—
72C2×#4318C2316yes—
73C2×#4313C2312yes—
74C2×#4313C2316yes—
75#66950C2×C416yes—
76C4⋊C4×D11C2×C416yes—
77#66943C2×C416yes—
78#66940C2×C416yes—
79#66936C2×C4112yes—
80#66932C2×C4112yes—
81C4×D44C2×C413yes—
82C4×D44C2311yescharacteristic
83#66925C2×C416yes—
84C42×D11C2316yes—
85#66923C2×C416yes—
86#66922C2×C413yes—
87#66922C2×C413yes—
88C4×Dic22C2×C413yes—
89C4×Dic22C2313yes—
90C4×Dic22C2316yes—
91C11×C4⋊C8C2313yes—
92C11×C4⋊C8C2313yes—
93C11×C22⋊C8C2316yes—
94C4×C8×C11C2313yes—
95C4×C8×C11C2313yes—
96C4×C8×C11C2311yescharacteristic
97C4×C8×C11C2313yes—
98C22⋊(C11⋊C8)C2316yes—
99(C2×D11)⋊C8C2312yes—
100(C2×D11)⋊C8C2316yes—
101#66879C2316yes—
102#66879C2316yes—
103Dic11⋊C8C2316yes—
104Dic11⋊C8C2316yes—
105Dic11⋊C8C23112yes—
106C8×Dic11C23112yes—
107C4⋊(C11⋊C8)C2313yes—
108C4⋊(C11⋊C8)C2316yes—
109C4⋊(C11⋊C8)C2311yescharacteristic
110C4×C11⋊C8C2316yes—
111#60345—111nomaximal, Sylow
112C11×#41—24no—
113C2×Q8×C11C22×C411yescharacteristic
114C2×D4×C11C22×C413yes—
115C22×C4×C11C22×C413yes—
116C22×C4×C11C22×C413yes—
117C22×C4×C11C2413yes—
118C2×C22⋊D11C22×C416yes—
119Q8×D11—28no—
120#4339—46no—
121C2×D44C22×C411yescharacteristic
122C2×C4×D11C22×C416yes—
123C2×C4×D11C22×C416yes—
124C2×C4×D11C2412yes—
125C2×Dic22C22×C413yes—
126C2×Dic22C22×C416yes—
127C2×C8×C11—26no—
128C2×C8×C11—43no—
129C2×C8×C11C2413yes—
130C2×C8×C11C2411yescharacteristic
131C2×C8×C11C2413yes—
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4C22×C413yes—
134C11×C4⋊C4C22×C413yes—
135C11×C22⋊C4C22×C416yes—
136C42×C11C22×C413yes—
137C42×C11C22×C413yes—
138C42×C11C2413yes—
139C42×C11C2411yescharacteristic
140C22⋊Dic11C22×C416yes—
141C22⋊Dic11C22×C4112yes—
142(C2×D11)⋊C4C22×C412yes—
143(C2×D11)⋊C4C22×C416yes—
144C4⋊Dic11C22×C411yescharacteristic
145C4⋊Dic11C22×C413yes—
146C4⋊Dic11C22×C416yes—
147C4⋊Dic11C22×C416yes—
148C4⋊Dic11C22×C416yes—
149Dic11⋊C4C22×C416yes—
150Dic11⋊C4C22×C416yes—
151Dic11⋊C4C22×C4112yes—
152C4×Dic11C22×C416yes—
153C4×Dic11C22×C416yes—
154C4×Dic11C2416yes—
155#4318—46no—
156C2×C11⋊C8C2412yes—
157C2×C11⋊C8C2416yes—
158#4313—24no—
159#4313—46no—
160#3482—111no—
161#2993—116no—
162#2991—113no—
163#2991—111no—
164#2986—113no—
165#2982—112no—
166#2969—116no—
167#2965—113no—
168C8×#41D1111yescharacteristic, complemented
169Q8×M16—112no—
170#2960—113no—
171C23×C11C23×C413yes—
172C22×D11C23×C412yes—
173Q8×C11#13114yes—
174D4×C11—26no—
175C2×C4×C11—26no—
176C2×C4×C11—26no—
177C2×C4×C11—23no—
178C2×C4×C11—23no—
179C2×C4×C11C23×C413yes—
180C2×C4×C11C23×C411yescharacteristic
181C2×C4×C11C23×C413yes—
182C2×C4×C11C23×C413yes—
183C2×C4×C11C23×C411yescharacteristic
184C2×C4×C11C2511yescharacteristic
185C22⋊D11—46no—
186C2×Dic11C23×C412yes—
187C2×Dic11C23×C416yes—
188C2×Dic11C23×C416yes—
189D44—22no—
190C4×D11—212no—
191C4×D11—22no—
192C4×D11—22no—
193C4×D11—46no—
194Dic22—212no—
195Dic22—26no—
196C8×C11—23no—
197C8×C11—23no—
198C8×C11—21no—
199C8×C112−1+412yes—
200C11⋊C8—22no—
201C11⋊C8—26no—
202#557—111no—
203#556—113no—
204#552—116no—
205D4×Q8—111no—
206#548—112no—
207#547—113no—
208#533—113no—
209#529—116no—
210C4×#41—113no—
211C4×#41C2×D1111yescharacteristic
212C2×C4×Q8—112no—
213#446—116no—
214#446—113no—
215#446—116no—
216#446—113no—
217C8×Q8—112no—
218C8×Q8—116no—
219C8×Q8—116no—
220C8×Q8—116no—
221C8×Q8C2×D1111yescharacteristic
222C8×Q8C2×D1111yescharacteristic
223#436—116no—
224#436—1112no—
225#436—111no—
226#436—113no—
227#435—116no—
228#435—116no—
229C8×D4C2×D1113yes—
230C8×D4C2×D1113yes—
231#433—1112no—
232#431—113no—
233#431—116no—
234#431—116no—
235#431C2×D1113yes—
236#424—116no—
237#423—113no—
238#423—116no—
239#405—116no—
240C4×M16—116no—
241C2×C4×C8C2×D1113yes—
242C22×C11—23no—
243C22×C11—23no—
244C22×C11—23no—
245C22×C11C24×C411yescharacteristic
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—22no—
249C4×C11—23no—
250C4×C11—21no—
251C4×C11—23no—
252C4×C11C2×#13116yes—
253C4×C11#56812yes—
254C4×C11C2×2−1+411yescharacteristic
255C4×C11#58511yescharacteristic
256Dic11—22no—
257Dic11—26no—
258Dic11—26no—
259C2×#41—113no—
260C2×#41C4×D1111yescharacteristic
261C22×Q8—112no—
262C2×M16—116no—
263C2×M16—112no—
264C2×M16—116no—
265C22×C8C22×D1113yes—
266C22×C8C22×D1113yes—
267C4⋊Q8—113no—
268C4⋊Q8—113no—
269#126—1112no—
270#125—116no—
271#125—116no—
272#124—116no—
273#123—1112no—
274C22⋊Q8—116no—
275C22⋊Q8—116no—
276C22⋊Q8—116no—
277#121—116no—
278C4×Q8—112no—
279C4×Q8—116no—
280C4×Q8—113no—
281C4×Q8—116no—
282C4×Q8—113no—
283C4×Q8C4×D1111yescharacteristic
284C4×Q8C22×D1111yescharacteristic
285C4×D4—116no—
286C4×D4—116no—
287C4×D4—113no—
288C4×D4—111no—
289C4×D4C4×D1113yes—
290C4×D4C22×D1113yes—
291#117—113no—
292#117—116no—
293#117—116no—
294#117C4×D1113yes—
295C2×C4⋊C4—116no—
296C2×C42—116no—
297C2×C42C22×D1113yes—
298C4⋊C8—1112no—
299C4⋊C8—116no—
300C4⋊C8—116no—
301C4⋊C8—116no—
302C4⋊C8—113no—
303C4⋊C8—111no—
304C4⋊C8C22×D1113yes—
305C4⋊C8C22×D1113yes—
306C22⋊C8—116no—
307C22⋊C8—112no—
308C22⋊C8—116no—
309C22⋊C8C22×D1116yes—
310#97—116no—
311#97—116no—
312C4×C8—1112no—
313C4×C8—116no—
314C4×C8C22×D1111yescharacteristic
315C4×C8C22×D1113yes—
316C4×C8C22×D1113yes—
317C4×C8C22×D1113yes—
318C2×C11—43no—
319C2×C11C4×2−1+411yescharacteristic
320C2×C11C22×#13111yescharacteristic
321C2×C11C2×#56811yescharacteristic
322D11—42no—
323#41—24no—
324#41—446no—
325C2×Q8—116no—
326C2×Q8—113no—
327C2×Q8—228no—
328C2×Q8C2×C4×D1111yescharacteristic
329C2×D4—116no—
330C2×D4—111no—
331C2×D4C2×C4×D1113yes—
332C22×C4—116no—
333C22×C4—112no—
334C22×C4—116no—
335C22×C4C2×C4×D1113yes—
336C22×C4C2×C4×D1113yes—
337C22×C4C23×D1113yes—
338M16—224no—
339M16—446no—
340M16—446no—
341C2×C8—26no—
342C2×C8—43no—
343C2×C8—112no—
344C2×C8—116no—
345C2×C8C23×D1113yes—
346C2×C8C23×D1111yescharacteristic
347C2×C8C23×D1113yes—
348C2×C8C23×D1111yescharacteristic
349C4⋊C4—116no—
350C4⋊C4—1112no—
351C4⋊C4—111no—
352C4⋊C4—116no—
353C4⋊C4—113no—
354C4⋊C4—116no—
355C4⋊C4—116no—
356C4⋊C4—116no—
357C4⋊C4C2×C4×D1113yes—
358C4⋊C4C2×C4×D1113yes—
359C22⋊C4—116no—
360C22⋊C4—1112no—
361C22⋊C4—112no—
362C22⋊C4—116no—
363C22⋊C4C2×C4×D1116yes—
364C42—116no—
365C42—116no—
366C42—116no—
367C42C2×C4×D1113yes—
368C42C2×C4×D1113yes—
369C42C23×D1113yes—
370C42C23×D1111yescharacteristic
371C11#6034511yescharacteristic, complemented, Sylow
372C23—112no—
373C23C22×C4×D1113yes—
374Q8—2212no—
375Q8—226no—
376Q8#6695414yes—
377D4—26no—
378D4—222no—
379D4—446no—
380C2×C4—26no—
381C2×C4—26no—
382C2×C4—23no—
383C2×C4—23no—
384C2×C4—112no—
385C2×C4—116no—
386C2×C4—116no—
387C2×C4—2212no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—446no—
391C2×C4C22×C4×D1113yes—
392C2×C4C22×C4×D1111yescharacteristic
393C2×C4C22×C4×D1113yes—
394C2×C4C22×C4×D1113yes—
395C2×C4C22×C4×D1111yescharacteristic
396C2×C4C24×D1111yescharacteristic
397C8—23no—
398C8—21no—
399C8—23no—
400C8—222no—
401C8—226no—
402C8#6704312yes—
403C22—23no—
404C22—23no—
405C22—23no—
406C22—222no—
407C22—222no—
408C22—222no—
409C22C23×C4×D1111yescharacteristic
410C4—21no—
411C4—23no—
412C4—23no—
413C4—226no—
414C4—226no—
415C4—222no—
416C4C2×#6695416yes—
417C4#1062328112yes—
418C4C2×#6704311yescharacteristic
419C4#1062345311yescharacteristic
420C2—43no—
421C2—442no—
422C2C4×#6704311yescharacteristic
423C2C22×#6695411yescharacteristic
424C2C2×#1062328111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC8×C11×#41C2
prime radical#13082238C2
cosocleC2×C4×C11C25
hypercenterC8×#41D11
hypocenterC11#60345
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
2. #13077766C2semidirect
3. #13077748C2semidirect
4. #13077745C2semidirect
5. #13077717C2semidirect
6. #13077695C2semidirect
7. #13077617C2semidirect
8. #13077582C2semidirect
9. Q8×#4313C2semidirect
10. #13077550C2semidirect
11. C8×C11×#41C2semidirect
168. C8×#41D11semidirect
371. C11#60345semidirect

Maximal subgroups

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

subgroupindex
#130822382
#130777662
#130777482
#130777452
#130777172
#130776952
#130776172
#130775822
Q8×#43132
#130775502
C8×C11×#412
#6034511