Finite Group Databasebeta

← #14657214

Subgroups — #14657214

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073570C211yesmaximal, characteristic
2#13069578C211yesmaximal, characteristic, complemented
3#13069380C211yesmaximal, characteristic, complemented
4#13068617C211yesmaximal, characteristic
5C2×#10622121C211yesmaximal, characteristic
6#13066455C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66999—21no—
10C2×#66999—21no—
11C2×C4×D44C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×#66885—21no—
15C2×#66881—21no—
16#10622605—22no—
17#10622601—21no—
18#10622589—21no—
19#10622548C2211yescharacteristic
20C4×C4⋊Dic11C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22C11×#332—22no—
23#10622189—21no—
24#10622189—21no—
25#10622167—22no—
26#10622121—22no—
27C22×Q8×C11—21no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D412yes—
38C2×C42×C11C2311yescharacteristic
39#66999—42no—
40#66999—42no—
41#66999—42no—
42#66999—42no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C2×C4×Dic11—21no—
55C22×C11⋊C8—21no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11⋊#95—21no—
65#66885—42no—
66#66881—42no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69#10420—111nomaximal, Sylow
70C23×D11—21no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—41no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44SD1612yes—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11#4111yescharacteristic
111(C2×D11)⋊C4—44no—
112(C2×D11)⋊C4—44no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—42no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11D812yes—
125C4⋊Dic11SD1612yes—
126Dic11⋊C4—44no—
127Dic11⋊C4—44no—
128C4×Dic11—41no—
129C4×Dic11—41no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133#2542—111no—
134#1990—111no—
135#1948—111no—
136#1802—111no—
137C2×#332D1111yescharacteristic, complemented
138C2×D4⋊C8—111no—
139#1279—111no—
140C23×C11#12011yescharacteristic
141C22×D11—22no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148Q8×C11—81no—
149Q8×C11—81no—
150Q8×C11—81no—
151Q8×C11—81no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12311yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11#12411yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×SD1611yescharacteristic
165C2×C4×C11C2×SD1611yescharacteristic
166C2×C4×C11#13511yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C2×C4×C11#13711yescharacteristic
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183D44—22no—
184D44—22no—
185D44—41no—
186D44—41no—
187C4×D11—81no—
188C4×D11—81no—
189C4×D11—81no—
190C4×D11—81no—
191C8×C11—42no—
192C8×C11—81no—
193C11⋊C8—42no—
194C2×C4⋊Q8C2×D1111yescharacteristic
195C2×C22⋊Q8—221no—
196C2×C22⋊Q8—221no—
197C2×C4×D4—111no—
198C2×#106—221no—
199C2×C4⋊C8C2×D1111yescharacteristic
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×#102—221no—
202C2×C4×C8—111no—
203#399—222no—
204#390—221no—
205#384—111no—
206#384—221no—
207C4×C4⋊C4—111no—
208#340—221no—
209#340—221no—
210#340—222no—
211#332—22no—
212D4⋊C8—222no—
213C22×C11#39411yescharacteristic
214C22×C11#44711yescharacteristic
215C22×C11#44811yescharacteristic
216C22×C11#45011yescharacteristic
217C22×C11#45211yescharacteristic
218C22×C11#45411yescharacteristic
219C22×C11#45611yescharacteristic
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—82no—
230C4×C11#45911yescharacteristic
231C4×C11#46011yescharacteristic
232C4×C11#46511yescharacteristic
233C4×C11#47011yescharacteristic
234C4×C11#48311yescharacteristic
235C4×C11#48511yescharacteristic
236C4×C11#48611yescharacteristic
237C4×C11#49011yescharacteristic
238Dic11—42no—
239Dic11—42no—
240Dic11—81no—
241Dic11—161no—
242C22×Q8—21no—
243C22×D4—111no—
244C23×C4—221no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—221no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C22⋊Q8—442no—
253C22⋊Q8—442no—
254C22⋊Q8—442no—
255C22⋊Q8—442no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—221no—
259C4×D4—221no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4D4412yes—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—221no—
273C2×C42—221no—
274C2×C42C22×D1111yescharacteristic
275#106—442no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8C22⋊D1112yes—
280#102—442no—
281C4×C8—221no—
282C4×C8—221no—
283#95—221no—
284C2×C11#162711yescharacteristic
285C2×C11#163511yescharacteristic
286C2×C11#164711yescharacteristic
287C2×C11#165111yescharacteristic
288C2×C11#203511yescharacteristic
289C2×C11#203811yescharacteristic
290C2×C11#204111yescharacteristic
291D11—82no—
292C24—221no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×D4—112no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—221no—
305C22×C4—22no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4—441no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4C2×D4411yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—222no—
326C2×C8—441no—
327C2×C8—441no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—112no—
333C4⋊C4—112no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—442no—
339C4⋊C4—444no—
340C4⋊C4—444no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C22⋊C4—444no—
346C22⋊C4—444no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C42—441no—
350C42—441no—
351C42#433911yescharacteristic
352C42#434111yescharacteristic
353C42#434111yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C11#1042011yescharacteristic, complemented, Sylow
356C23—222no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23#6693511yescharacteristic
364Q8—81no—
365Q8—81no—
366Q8—81no—
367Q8—81no—
368D4—222no—
369D4—222no—
370D4—441no—
371D4—441no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4—881no—
392C2×C4—881no—
393C2×C4#6693611yescharacteristic
394C2×C4#6693811yescharacteristic
395C2×C4#6693911yescharacteristic
396C2×C4D8×D1111yescharacteristic
397C2×C4#6696411yescharacteristic
398C2×C4SD16×D1111yescharacteristic
399C2×C4SD16×D1111yescharacteristic
400C2×C4#6696711yescharacteristic
401C2×C4#6696911yescharacteristic
402C2×C4#6697111yescharacteristic
403C2×C4#6697111yescharacteristic
404C2×C4#6698311yescharacteristic
405C2×C4#6699111yescharacteristic
406C2×C4#6699211yescharacteristic
407C8—42no—
408C8—81no—
409C8—442no—
410C22—442no—
411C22—442no—
412C22—442no—
413C22—881no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22#1062236511yescharacteristic
418C22#1062236611yescharacteristic
419C22#1062238611yescharacteristic
420C22#1062238911yescharacteristic
421C22#1062241911yescharacteristic
422C22#1062242311yescharacteristic
423C22#1062257411yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—442no—
428C4—442no—
429C4—881no—
430C4—1761no—
431C4#1062237311yescharacteristic
432C4#1062237711yescharacteristic
433C4#1062241811yescharacteristic
434C4#1062242811yescharacteristic
435C4#1062276311yescharacteristic
436C4#1062277611yescharacteristic
437C4#1062278411yescharacteristic
438C4#1062280211yescharacteristic
439C2—882no—
440C2#1306772011yescharacteristic
441C2#1306776811yescharacteristic
442C2#1306785211yescharacteristic
443C2#1306788011yescharacteristic
444C2#1306981111yescharacteristic
445C2#1306983411yescharacteristic
446C2#1306984911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#332D11
hypocenterC11#10420
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #13069578C2semidirect
3. #13069380C2semidirect
6. #13066455C2semidirect
7. C2×C11×#332C2semidirect
137. C2×#332D11semidirect
355. C11#10420semidirect

Maximal subgroups

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

subgroupindex
#130735702
#130695782
#130693802
#130686172
C2×#106221212
#130664552
C2×C11×#3322
#1042011