Finite Group Databasebeta

← #14649465

Subgroups — #14649465

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622450C211yesmaximal, 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—
10C22×#4313—21no—
11C2×C42×D11C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14#10622843—21no—
15C2×(C2×D11)⋊C8—21no—
16C2×Dic11⋊C8—21no—
17#10622600—21no—
18#10622600C412yes—
19#10622586—21no—
20#10622586C412yes—
21#10622548C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622450—22no—
25#10622450—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—
54C2×#4313—24no—
55C2×#4313—42no—
56C2×#4313—42no—
57C42×D11—21no—
58C42×D11—21no—
59C42×D11—21no—
60C42×D11—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11⋊#95—22no—
66C11⋊#95—22no—
67(C2×D11)⋊C8—42no—
68Dic11⋊C8—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73#9139—111nomaximal, Sylow
74C23×D11C22⋊C411yescharacteristic
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C22×C4×C11—22no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C2×C4×D11—22no—
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—21no—
101C2×C4×D11—21no—
102C2×C4×D11—41no—
103C2×C4×D11D812yes—
104C2×C4×D11SD1612yes—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11#4111yescharacteristic
119(C2×D11)⋊C4—44no—
120C4⋊Dic11—42no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—44no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C4×Dic11—21no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138#4313—48no—
139C2×#423—111no—
140#2857—111no—
141#1797—111no—
142C2×#332—111no—
143C2×#332D1111yescharacteristic, complemented
144#1296—111no—
145#1296—111no—
146C23×C11C2×C22⋊C411yescharacteristic
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11#10212yes—
154Q8×C11—81no—
155Q8×C11—81no—
156Q8×C11—81no—
157Q8×C11—81no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12311yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C2×SD1611yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11#13711yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C2×C4×C11#13711yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11#10112yes—
188C2×Dic11#10212yes—
189C4×D11—22no—
190C4×D11—22no—
191C4×D11—22no—
192C4×D11—22no—
193C4×D11—42no—
194C4×D11—42no—
195C4×D11—41no—
196C4×D11—41no—
197C4×D11—41no—
198C4×D11—41no—
199C8×C11—42no—
200C8×C11—81no—
201C11⋊C8—42no—
202C11⋊C8—81no—
203C22×M16—221no—
204C2×C4⋊Q8C2×D1111yescharacteristic
205C2×C22⋊Q8—221no—
206C22×C42—111no—
207#423—222no—
208#423—222no—
209C2×C4⋊C8—111no—
210C2×C4⋊C8—111no—
211C2×C4⋊C8—221no—
212C2×C4⋊C8C2×D1111yescharacteristic
213C2×C4⋊C8C2×D1111yescharacteristic
214C2×C22⋊C8—221no—
215#391—221no—
216#389—112no—
217#389—221no—
218#384—111no—
219#380—112no—
220#380—221no—
221#336—221no—
222#332—22no—
223#332—222no—
224C22×C11#38611yescharacteristic
225C22×C11C2×#10111yescharacteristic
226C22×C11#41311yescharacteristic
227C22×C11C2×#10211yescharacteristic
228C22×C11#41711yescharacteristic
229C22×C11#41711yescharacteristic
230C22×C11#41911yescharacteristic
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—41no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—82no—
241C4×C11#44711yescharacteristic
242C4×C11#44811yescharacteristic
243C4×C11#46811yescharacteristic
244C4×C11#46811yescharacteristic
245C4×C11#47011yescharacteristic
246C4×C11#47011yescharacteristic
247C4×C11#48011yescharacteristic
248C4×C11#48111yescharacteristic
249Dic11—22no—
250Dic11—22no—
251Dic11—41no—
252Dic11—82no—
253C22×Q8—21no—
254C23×C4—111no—
255C23×C4—111no—
256C23×C4—111no—
257C2×M16—224no—
258C2×M16—442no—
259C2×M16—442no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—221no—
263C22×C8—221no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C22⋊Q8—442no—
269C22⋊Q8—442no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4C4×D1112yes—
276C2×C22⋊C4—222no—
277C2×C42—111no—
278C2×C42—111no—
279C2×C42—111no—
280C2×C42—221no—
281C2×C42—221no—
282C2×C42—221no—
283C2×C42—221no—
284C2×C42C22×D1111yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—112no—
289C4⋊C8—224no—
290C4⋊C8—221no—
291C4⋊C8—221no—
292C4⋊C8—221no—
293C4⋊C8C22⋊D1112yes—
294C22⋊C8—442no—
295#95—222no—
296#95—222no—
297C2×C11#154611yescharacteristic
298C2×C11#154711yescharacteristic
299C2×C11#155911yescharacteristic
300C2×C11#156111yescharacteristic
301C2×C11#187411yescharacteristic
302C2×C11#189411yescharacteristic
303C2×C11#190111yescharacteristic
304D11—42no—
305C24—111no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C22×C4—22no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—112no—
316C22×C4—112no—
317C22×C4—111no—
318C22×C4—222no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—222no—
332C22×C4—441no—
333C22×C4C2×C4×D1111yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4D4×D1111yescharacteristic
336M16—448no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—222no—
344C2×C8—441no—
345C2×C8—441no—
346C2×C8—441no—
347C2×C8—441no—
348C2×C8—441no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—442no—
354C4⋊C4—444no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C4⋊C4—441no—
359C22⋊C4—444no—
360C42—221no—
361C42—221no—
362C42—221no—
363C42—221no—
364C42—221no—
365C42—221no—
366C42#433911yescharacteristic
367C42D4×D1111yescharacteristic
368C42#434111yescharacteristic
369C42C2×C22⋊D1111yescharacteristic
370C11#913911yescharacteristic, complemented, Sylow
371C23—112no—
372C23—221no—
373C23—221no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23C22⋊C4×D1111yescharacteristic
379Q8—81no—
380Q8—81no—
381Q8—81no—
382Q8—81no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—112no—
389C2×C4—112no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4(C22⋊D11)⋊C411yescharacteristic
411C2×C4#6693611yescharacteristic
412C2×C4#6693711yescharacteristic
413C2×C4D8×D1111yescharacteristic
414C2×C4#6696411yescharacteristic
415C2×C4SD16×D1111yescharacteristic
416C2×C4#6696711yescharacteristic
417C2×C4#6696811yescharacteristic
418C2×C4#6696811yescharacteristic
419C2×C4#6697111yescharacteristic
420C2×C4#6697111yescharacteristic
421C2×C4C4×C22⋊D1111yescharacteristic
422C2×C4#6699011yescharacteristic
423C2×C4#6699111yescharacteristic
424C8—42no—
425C8—81no—
426C8—442no—
427C8—881no—
428C22—222no—
429C22—222no—
430C22—222no—
431C22—441no—
432C22—441no—
433C22—441no—
434C22—441no—
435C22D11×#10111yescharacteristic
436C22#1062236411yescharacteristic
437C22D11×#10211yescharacteristic
438C22#1062238411yescharacteristic
439C22#1062241511yescharacteristic
440C22#1062241611yescharacteristic
441C22#1062256911yescharacteristic
442C4—21no—
443C4—21no—
444C4—82no—
445C4—222no—
446C4—222no—
447C4—441no—
448C4—882no—
449C4#1062238711yescharacteristic
450C4#1062239011yescharacteristic
451C4#1062242511yescharacteristic
452C4#1062242911yescharacteristic
453C4#1062276911yescharacteristic
454C4#1062278311yescharacteristic
455C4#1062278711yescharacteristic
456C4#1062280211yescharacteristic
457C2—442no—
458C2#1306728611yescharacteristic
459C2#1306729211yescharacteristic
460C2#1306734511yescharacteristic
461C2#1306735211yescharacteristic
462C2#1306893011yescharacteristic
463C2#1306904611yescharacteristic
464C2#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#9139
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
143. C2×#332D11semidirect
370. C11#9139semidirect

Maximal subgroups

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

subgroupindex
C2×#106224502
#130769632
#130685932
C2×#106221852
#130665002
C2×C11×#3322
#913911