Finite Group Databasebeta

← #14650010

Subgroups — #14650010

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622628C211yesmaximal, characteristic
2#13069422C211yesmaximal, characteristic, complemented
3#13068616C211yesmaximal, characteristic, complemented
4C2×#10622123C211yesmaximal, characteristic, complemented
5#13066500C211yesmaximal, characteristic, complemented
6#13066451C211yesmaximal, characteristic, complemented
7C2×C11×#436C211yesmaximal, characteristic, complemented
8C22×C11×M16—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C22×#4323—21no—
11C2×#66927C2211yescharacteristic
12C11×#436—22no—
13C11×#436—22no—
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C22⋊C8—21no—
16C2×C4×C8×C11C2211yescharacteristic
17C2×#66896—21no—
18C2×#66885—21no—
19C2×#66885—21no—
20#10622628—22no—
21#10622628C414yescomplemented
22C2×#66873—21no—
23#10622548C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26#10622167—21no—
27#10622123—22no—
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C2×C11×M16—24no—
34C2×C11×M16—42no—
35C2×C11×M16—42no—
36C22×C8×C11—21no—
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11C2×C412yes—
42C4×D4×C11D412yes—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—21no—
45C2×C42×C11C2311yescharacteristic
46C2×#4323—24no—
47C2×#4323—42no—
48C2×#4323—42no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54#66927—21no—
55#66927—21no—
56#66927—21no—
57#66927C2×C412yes—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11×C22⋊C8—24no—
61C4×C8×C11—21no—
62C4×C8×C11—21no—
63#66896—42no—
64#66885—42no—
65#66885—42no—
66#66873—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)C2×C412yes—
71#9229—111nomaximal, Sylow
72C24×C11—21no—
73C23×D11—41no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11C22⋊C412yes—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—41no—
91C2×D44—22no—
92C2×D44—22no—
93C2×D44—22no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—81no—
106C2×D44—81no—
107C11×M16—48no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—22no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11D812yescomplemented
117C11×C4⋊C4—21no—
118C11×C4⋊C4C22⋊C412yes—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—22no—
121C42×C11C22×C411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125#4323—48no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C4⋊Dic11—81no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×#459—111no—
138C2×#436D1111yescharacteristic, complemented
139#1957—111no—
140#1802—111no—
141C2×#331—111no—
142#1296—111no—
143#1277—111no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#12111yescharacteristic
152C22×D11—42no—
153C22×D11—81no—
154C22×D11—81no—
155C22×D11—81no—
156C22×D11—81no—
157C22×D11—81no—
158C22×D11—81no—
159D4×C11—22no—
160D4×C11—22no—
161D4×C11—41no—
162D4×C11—41no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11C2×C22⋊C411yescharacteristic
173C2×C4×C11C4×D411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12311yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11#13511yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C11#13711yescharacteristic
186C2×Dic11—81no—
187C2×Dic11—81no—
188C2×Dic11—81no—
189D44—42no—
190D44—42no—
191D44—42no—
192D44—42no—
193D44—82no—
194D44—82no—
195D44—81no—
196D44—81no—
197D44—81no—
198D44—81no—
199C8×C11—22no—
200C8×C11—42no—
201C8×C11—41no—
202C11⋊C8—42no—
203C11⋊C8—81no—
204C22×D8—221no—
205C22×M16—21no—
206C2×#127—111no—
207C2×C4×D4C2×D1111yescharacteristic
208#459—114no—
209#459—222no—
210#436—22no—
211#436—22no—
212C2×C4⋊C8—111no—
213C2×C4⋊C8—111no—
214C2×C4⋊C8C2×D1111yescharacteristic
215C2×#102—221no—
216C2×#102—221no—
217C2×#102—221no—
218C2×#102—221no—
219C2×C22⋊C8—21no—
220C2×C4×C8C2×D1111yescharacteristic
221#384—111no—
222#340—221no—
223#331—222no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11#38611yescharacteristic
232C22×C11#45911yescharacteristic
233C22×C11#46311yescharacteristic
234C22×C11#46811yescharacteristic
235C22×C11#46911yescharacteristic
236C22×C11#47111yescharacteristic
237C22×C11#47211yescharacteristic
238C2×D11—82no—
239C2×D11—82no—
240C2×D11—82no—
241C2×D11—161no—
242C2×D11—161no—
243C2×D11—161no—
244C2×D11—161no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—42no—
248C4×C11#41711yescharacteristic
249C4×C11#41811yescharacteristic
250C4×C11C4×D811yescharacteristic
251C4×C11#44211yescharacteristic
252C4×C11#44711yescharacteristic
253C4×C11#44911yescharacteristic
254C4×C11#46811yescharacteristic
255C4×C11#46911yescharacteristic
256Dic11—161no—
257C22×D4—221no—
258C22×D4—221no—
259C22×D4—221no—
260C22×D4D4411yescharacteristic
261C23×C4—21no—
262C2×D8—224no—
263C2×D8—442no—
264C2×D8—442no—
265C2×M16—24no—
266C2×M16—42no—
267C2×M16—42no—
268C22×C8—21no—
269C22×C8—221no—
270C22×C8—221no—
271C22×C8C22⋊D1111yescharacteristic
272C22×C8C22⋊D1111yescharacteristic
273#127—112no—
274#127—221no—
275#127—221no—
276#127—221no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4C4×D1112yes—
280C4×D4C22⋊D1112yes—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4D4411yescharacteristic
285C2×C22⋊C4—21no—
286C2×C42C22×D1111yescharacteristic
287C4⋊C8—21no—
288C4⋊C8—112no—
289C4⋊C8—221no—
290C4⋊C8—221no—
291C4⋊C8—221no—
292C4⋊C8C22⋊D1112yes—
293#102—224no—
294#102—442no—
295#102—442no—
296#102—442no—
297C22⋊C8—24no—
298C4×C8—21no—
299C4×C8—21no—
300C2×C11—82no—
301C2×C11#168511yescharacteristic
302C2×C11#168711yescharacteristic
303C2×C11#169711yescharacteristic
304C2×C11#170111yescharacteristic
305C2×C11#187911yescharacteristic
306C2×C11#189511yescharacteristic
307C2×C11#190711yescharacteristic
308D11—162no—
309C24—21no—
310C24—441no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—222no—
317C2×D4—222no—
318C2×D4—222no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—441no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4—441no—
327C2×D4—441no—
328C2×D4—441no—
329C2×D4—441no—
330C2×D4—881no—
331C2×D4—881no—
332C2×D4(C2×D11)⋊C412yes—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—441no—
341C22×C4C2×D4411yescharacteristic
342C22×C4#433911yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344D8—448no—
345M16—48no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—222no—
355C2×C8—441no—
356C2×C8—441no—
357C2×C8—441no—
358C2×C8—441no—
359C2×C8—441no—
360C2×C8#432312yescomplemented
361C4⋊C4—21no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—441no—
365C4⋊C4—441no—
366C4⋊C4—881no—
367C4⋊C4(C2×D11)⋊C412yes—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C42C2×C4×D1111yescharacteristic
371C42#433911yescharacteristic
372C42C2×C22⋊D1111yescharacteristic
373C42C2×C22⋊D1111yescharacteristic
374C11#922911yescharacteristic, complemented, Sylow
375C23—22no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—442no—
383C23—881no—
384C23—881no—
385C23—881no—
386C23—881no—
387C23—881no—
388C23—881no—
389C23#6698311yescharacteristic
390D4—22no—
391D4—22no—
392D4—41no—
393D4—41no—
394D4—442no—
395D4—442no—
396D4—442no—
397D4—442no—
398D4—882no—
399D4—882no—
400D4—881no—
401D4—881no—
402D4—881no—
403D4—881no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—881no—
414C2×C4—881no—
415C2×C4—881no—
416C2×C4#6696111yescharacteristic
417C2×C4#6696111yescharacteristic
418C2×C4#6696111yescharacteristic
419C2×C4#6696211yescharacteristic
420C2×C4C2×(C2×D11)⋊C411yescharacteristic
421C2×C4C4×C22⋊D1111yescharacteristic
422C2×C4C4×C22⋊D1111yescharacteristic
423C2×C4#6698211yescharacteristic
424C2×C4#6698311yescharacteristic
425C2×C4C2×#432311yescharacteristic
426C2×C4#6698511yescharacteristic
427C2×C4#6700211yescharacteristic
428C2×C4#6700311yescharacteristic
429C2×C4#6700611yescharacteristic
430C8—22no—
431C8—42no—
432C8—41no—
433C8—442no—
434C8—881no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—882no—
443C22—882no—
444C22—882no—
445C22—1761no—
446C22—1761no—
447C22—1761no—
448C22—1761no—
449C22#1062262811yescharacteristic
450C22#1062262911yescharacteristic
451C22#1062274711yescharacteristic
452C22#1062274811yescharacteristic
453C22#1062275411yescharacteristic
454C22#1062275511yescharacteristic
455C22#1062282611yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—1761no—
460C4C4×#432311yescharacteristic
461C4#1062262711yescharacteristic
462C4#1062274411yescharacteristic
463C4#1062274611yescharacteristic
464C4#1062274711yescharacteristic
465C4#1062274811yescharacteristic
466C4#1062283011yescharacteristic
467C4#1062285111yescharacteristic
468C2—82no—
469C2—1762no—
470C2#1306808111yescharacteristic
471C2#1306809511yescharacteristic
472C2#1306814911yescharacteristic
473C2#1306817711yescharacteristic
474C2#1306896411yescharacteristic
475C2#1306905411yescharacteristic
476C2#1306912411yescharacteristic
subgroupG/H
centerC23#66983
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#436C2
socleC23×C11#121
prime radicalC2×#10622628C2
cosocleC2×C42×C11C23
hypercenterC2×#436D11
hypocenterC11#9229
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. #13069422C2semidirect
3. #13068616C2semidirect
4. C2×#10622123C2semidirect
5. #13066500C2semidirect
6. #13066451C2semidirect
7. C2×C11×#436C2semidirect
21. #10622628C4semidirect
116. C2×C8×C11D8semidirect
138. C2×#436D11semidirect
360. C2×C8#4323semidirect
374. C11#9229semidirect

Maximal subgroups

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

subgroupindex
C2×#106226282
#130694222
#130686162
C2×#106221232
#130665002
#130664512
C2×C11×#4362
#922911