Finite Group Databasebeta

← #14657306

Subgroups — #14657306

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073534C211yesmaximal, characteristic
2#13068772C211yesmaximal, characteristic, complemented
3#13068613C211yesmaximal, characteristic
4C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic, complemented
7C11×#1803C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66999—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103—21no—
13C11×#384C2211yescharacteristic
14#10622607—22no—
15#10622600—21no—
16C2×#66873—21no—
17C2×#66872—22no—
18#10622552—21no—
19#10622548C2211yescharacteristic
20#10622541—21no—
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#340—21no—
24Q8⋊(C11⋊C8)—22no—
25#10622167—21no—
26#10622121—22no—
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42#66999—42no—
43#66999—42no—
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—22no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11D412yes—
51C2×Dic11⋊C4—22no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×#103—42no—
61C11⋊#95—22no—
62#66873—42no—
63#66872—44no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8D412yes—
68#10435—111nomaximal, Sylow
69C23×D11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11SD1612yes—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—22no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44SD1612yes—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C42×C11—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114(C2×D11)⋊C4—44no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—82no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—42no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—44no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#2538—111no—
133#1844—111no—
134#1803D1111yescharacteristic, complemented
135#1802—111no—
136C2×Q8⋊C8—111no—
137C2×D4⋊C8—111no—
138#1296—111no—
139C23×C11#12011yescharacteristic
140C22×D11—22no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—41no—
150Q8×C11—41no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C2×C4×C11#12411yescharacteristic
168C2×C4×C11C2×SD1611yescharacteristic
169C2×C4×C11C2×SD1611yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C2×C4×C11#13711yescharacteristic
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182D44—22no—
183D44—22no—
184D44—41no—
185D44—41no—
186C4×D11—81no—
187C4×D11—81no—
188C4×D11—81no—
189C4×D11—81no—
190C8×C11—81no—
191C11⋊C8—24no—
192C11⋊C8—81no—
193C2×C22⋊Q8—221no—
194C2×C4×Q8C2×D1111yescharacteristic
195C2×C4×D4—111no—
196C2×#106—222no—
197C2×C4⋊C8—111no—
198C2×C4⋊C8C2×D1111yescharacteristic
199C2×#103—21no—
200C2×#102—221no—
201C2×C4×C8—111no—
202#396—222no—
203#390—221no—
204#389—221no—
205#384—111no—
206#384C2×D1111yescharacteristic
207#380—221no—
208#340—21no—
209#340—221no—
210Q8⋊C8—222no—
211D4⋊C8—222no—
212C22×C11#39411yescharacteristic
213C22×C11#44811yescharacteristic
214C22×C11#44911yescharacteristic
215C22×C11#45011yescharacteristic
216C22×C11#45211yescharacteristic
217C22×C11#45311yescharacteristic
218C22×C11#45611yescharacteristic
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—42no—
229C4×C11—81no—
230C4×C11—161no—
231C4×C11#46511yescharacteristic
232C4×C11#46511yescharacteristic
233C4×C11#46911yescharacteristic
234C4×C11#47011yescharacteristic
235C4×C11#48111yescharacteristic
236C4×C11#48211yescharacteristic
237C4×C11#48311yescharacteristic
238C4×C11#48511yescharacteristic
239Dic11—82no—
240Dic11—81no—
241C22×Q8C22⋊D1111yescharacteristic
242C22×D4—111no—
243C23×C4—221no—
244C22×C8—21no—
245C22×C8—221no—
246C22×C8—221no—
247C22⋊Q8—442no—
248C22⋊Q8—442no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×D4—221no—
254C4×D4—221no—
255C4×D4—221no—
256C4×D4—221no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—112no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4C22⋊D1111yescharacteristic
267C2×C22⋊C4—222no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—222no—
270C2×C42—21no—
271C2×C42C22×D1111yescharacteristic
272#106—444no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—221no—
276C4⋊C8—221no—
277#103—42no—
278#102—442no—
279C4×C8—112no—
280C4×C8—221no—
281#95—222no—
282C2×C11#162211yescharacteristic
283C2×C11#163111yescharacteristic
284C2×C11#165111yescharacteristic
285C2×C11#165211yescharacteristic
286C2×C11#203411yescharacteristic
287C2×C11#203511yescharacteristic
288C2×C11#203911yescharacteristic
289D11—82no—
290C24—221no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8#432512yes—
297C2×D4—112no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—221no—
307C22×C4—222no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4—441no—
314C22×C4D4×D1111yescharacteristic
315C22×C4D4×D1111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—441no—
324C2×C8—441no—
325C2×C8—441no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C4⋊C4—442no—
338C4⋊C4—444no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C22⋊C4—444no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—882no—
347C42—41no—
348C42—41no—
349C42#433911yescharacteristic
350C42#433911yescharacteristic
351C42D4×D1111yescharacteristic
352C42#434111yescharacteristic
353C11#1043511yescharacteristic, complemented, Sylow
354C23—222no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23#6699011yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—41no—
365Q8—41no—
366D4—222no—
367D4—222no—
368D4—441no—
369D4—441no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—441no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4#6693611yescharacteristic
392C2×C4#6693711yescharacteristic
393C2×C4#6693711yescharacteristic
394C2×C4#6693811yescharacteristic
395C2×C4SD16×D1111yescharacteristic
396C2×C4#6696811yescharacteristic
397C2×C4#6697111yescharacteristic
398C2×C4#6697211yescharacteristic
399C2×C4#6698211yescharacteristic
400C2×C4#6698511yescharacteristic
401C2×C4#6699211yescharacteristic
402C2×C4C2×#432511yescharacteristic
403C2×C4#6700211yescharacteristic
404C2×C4#6700311yescharacteristic
405C8—81no—
406C8—224no—
407C8—881no—
408C22—442no—
409C22—442no—
410C22—442no—
411C22—881no—
412C22—881no—
413C22—881no—
414C22—881no—
415C22#1062257211yescharacteristic
416C22#1062265011yescharacteristic
417C22#1062265911yescharacteristic
418C22#1062278311yescharacteristic
419C22#1062280011yescharacteristic
420C22#1062281111yescharacteristic
421C22#1062281811yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—161no—
427C4—882no—
428C4—881no—
429C4#1062241811yescharacteristic
430C4#1062242011yescharacteristic
431C4#1062242711yescharacteristic
432C4#1062242911yescharacteristic
433C4#1062258111yescharacteristic
434C4#1062261611yescharacteristic
435C4#1062265211yescharacteristic
436C4#1062266111yescharacteristic
437C2—882no—
438C2#1306768711yescharacteristic
439C2#1306774111yescharacteristic
440C2#1306787811yescharacteristic
441C2#1306788411yescharacteristic
442C2#1306980511yescharacteristic
443C2#1306981011yescharacteristic
444C2#1306983811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1803C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1803D11
hypocenterC11#10435
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #13068772C2semidirect
4. C2×Q8⋊(C11⋊C8)C2semidirect
6. #13066500C2semidirect
7. C11×#1803C2semidirect
134. #1803D11semidirect
353. C11#10435semidirect

Maximal subgroups

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

subgroupindex
#130735342
#130687722
#130686132
C2×Q8⋊(C11⋊C8)2
C2×#106221212
#130665002
C11×#18032
#1043511