Finite Group Databasebeta

← #14649430

Subgroups — #14649430

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622446C211yesmaximal, characteristic
2#13076963C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, characteristic, complemented
5#13066500C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66999—21no—
10C2×C42×D11C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622843—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×(C2×D11)⋊C8—21no—
16C2×C8×Dic11—21no—
17#10622600—21no—
18#10622600C412yes—
19#10622586—21no—
20#10622586C412yes—
21#10622548C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622446—22no—
25#10622446—22no—
26C11×#332—22no—
27#10622188—21no—
28#10622185—22no—
29C22×Q8×C11—21no—
30C22×C4×D11C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C412yes—
41C2×C42×C11C2311yescharacteristic
42#66999—42no—
43#66999—42no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11C2×C412yes—
48C2×Dic11⋊C4—22no—
49C2×C4×Dic11C2×C411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C2×C4×Dic11D411yescharacteristic
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C42×D11—21no—
55C42×D11—21no—
56C42×D11—21no—
57C42×D11—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11⋊#95—22no—
63C11⋊#95—22no—
64(C2×D11)⋊C8—24no—
65(C2×D11)⋊C8—42no—
66C8×Dic11—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71#9132—111nomaximal, Sylow
72C23×D11C22⋊C411yescharacteristic
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C22×C4×C11—22no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C2×C4×D11—22no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C2×C4×D11—21no—
100C2×C4×D11—41no—
101C2×C4×D11SD1612yes—
102C2×C4×D11Q1612yes—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11#4111yescharacteristic
117(C2×D11)⋊C4—44no—
118C4⋊Dic11—42no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123Dic11⋊C4—44no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×#431—111no—
137#2857—111no—
138#1797—111no—
139C2×#332—111no—
140C2×#332D1111yescharacteristic, complemented
141#1296—111no—
142#1296—111no—
143C23×C11C2×C22⋊C411yescharacteristic
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11#10312yes—
151Q8×C11—81no—
152Q8×C11—81no—
153Q8×C11—81no—
154Q8×C11—81no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×C4×C11C2×SD1611yescharacteristic
167C2×C4×C11C2×Q1611yescharacteristic
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11#10112yes—
185C2×Dic11#10312yes—
186C4×D11—22no—
187C4×D11—22no—
188C4×D11—22no—
189C4×D11—22no—
190C4×D11—42no—
191C4×D11—42no—
192C4×D11—41no—
193C4×D11—41no—
194C4×D11—41no—
195C4×D11—41no—
196C8×C11—42no—
197C8×C11—81no—
198C11⋊C8—42no—
199C11⋊C8—81no—
200C2×C4⋊Q8C2×D1111yescharacteristic
201C2×C22⋊Q8—221no—
202C22×C42—111no—
203#431—222no—
204#431—222no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8—111no—
207C2×C4⋊C8C2×D1111yescharacteristic
208C2×C4⋊C8C2×D1111yescharacteristic
209C2×C22⋊C8—221no—
210C2×C22⋊C8—221no—
211C2×C4×C8—221no—
212#391—221no—
213#389—112no—
214#389—221no—
215#384—111no—
216#380—112no—
217#380—221no—
218#336—221no—
219#332—22no—
220#332—222no—
221C22×C11#38611yescharacteristic
222C22×C11C2×#10111yescharacteristic
223C22×C11#41311yescharacteristic
224C22×C11C2×#10311yescharacteristic
225C22×C11#41611yescharacteristic
226C22×C11#41611yescharacteristic
227C22×C11#41811yescharacteristic
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—82no—
238C4×C11#44911yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#46511yescharacteristic
241C4×C11#46511yescharacteristic
242C4×C11#46711yescharacteristic
243C4×C11#46711yescharacteristic
244C4×C11#48211yescharacteristic
245C4×C11#48211yescharacteristic
246Dic11—22no—
247Dic11—22no—
248Dic11—41no—
249Dic11—82no—
250C22×Q8—21no—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4—111no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—221no—
257C22×C8—221no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C22⋊Q8—442no—
263C22⋊Q8—442no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—112no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4C4×D1112yes—
270C2×C22⋊C4—222no—
271C2×C42—111no—
272C2×C42—111no—
273C2×C42—111no—
274C2×C42—221no—
275C2×C42—221no—
276C2×C42—221no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—112no—
283C4⋊C8—221no—
284C4⋊C8—221no—
285C4⋊C8—221no—
286C4⋊C8C22⋊D1112yes—
287C22⋊C8—224no—
288C22⋊C8—442no—
289C4×C8—224no—
290#95—222no—
291#95—222no—
292C2×C11#154211yescharacteristic
293C2×C11#154411yescharacteristic
294C2×C11#154911yescharacteristic
295C2×C11#155311yescharacteristic
296C2×C11#187511yescharacteristic
297C2×C11#189211yescharacteristic
298C2×C11#190111yescharacteristic
299D11—42no—
300C24—111no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C22×C4—22no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—112no—
311C22×C4—112no—
312C22×C4—111no—
313C22×C4—222no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—222no—
327C22×C4—441no—
328C22×C4C2×C4×D1111yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—222no—
338C2×C8—441no—
339C2×C8—441no—
340C2×C8—441no—
341C2×C8—441no—
342C2×C8—441no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—442no—
348C4⋊C4—444no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—444no—
354C42—221no—
355C42—221no—
356C42—221no—
357C42—221no—
358C42—221no—
359C42—221no—
360C42#433911yescharacteristic
361C42D4×D1111yescharacteristic
362C42#434111yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C11#913211yescharacteristic, complemented, Sylow
365C23—112no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23C22⋊C4×D1111yescharacteristic
373Q8—81no—
374Q8—81no—
375Q8—81no—
376Q8—81no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—112no—
383C2×C4—112no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4(C22⋊D11)⋊C411yescharacteristic
405C2×C4#6693611yescharacteristic
406C2×C4#6693711yescharacteristic
407C2×C4#6696411yescharacteristic
408C2×C4#6696511yescharacteristic
409C2×C4SD16×D1111yescharacteristic
410C2×C4#6696711yescharacteristic
411C2×C4#6696911yescharacteristic
412C2×C4#6696911yescharacteristic
413C2×C4Q16×D1111yescharacteristic
414C2×C4#6697211yescharacteristic
415C2×C4C4×C22⋊D1111yescharacteristic
416C2×C4#6699011yescharacteristic
417C2×C4#6699111yescharacteristic
418C8—42no—
419C8—81no—
420C8—442no—
421C8—881no—
422C22—222no—
423C22—222no—
424C22—222no—
425C22—441no—
426C22—441no—
427C22—441no—
428C22—441no—
429C22D11×#10111yescharacteristic
430C22#1062236411yescharacteristic
431C22#1062238311yescharacteristic
432C22#1062238511yescharacteristic
433C22D11×#10311yescharacteristic
434C22#1062241711yescharacteristic
435C22#1062256911yescharacteristic
436C4—21no—
437C4—21no—
438C4—82no—
439C4—222no—
440C4—222no—
441C4—441no—
442C4—882no—
443C4#1062239211yescharacteristic
444C4#1062239711yescharacteristic
445C4#1062242011yescharacteristic
446C4#1062242611yescharacteristic
447C4#1062277111yescharacteristic
448C4#1062278411yescharacteristic
449C4#1062278511yescharacteristic
450C4#1062280111yescharacteristic
451C2—442no—
452C2#1306727211yescharacteristic
453C2#1306727911yescharacteristic
454C2#1306729911yescharacteristic
455C2#1306732011yescharacteristic
456C2#1306893511yescharacteristic
457C2#1306903611yescharacteristic
458C2#1306908111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#9132
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
4. C2×#10622185C2semidirect
5. #13066500C2semidirect
6. #13066500C2semidirect
7. C2×C11×#332C2semidirect
140. C2×#332D11semidirect
364. C11#9132semidirect

Maximal subgroups

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

subgroupindex
C2×#106224462
#130769632
#130685932
C2×#106221852
#130665002
C2×C11×#3322
#913211