Finite Group Databasebeta

← #14656083

Subgroups — #14656083

Order 2816.

676 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622461C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13073986C211yesmaximal, characteristic, complemented
4#13069422C211yesmaximal, characteristic
5C2×#10622094C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C22×#4325—21no—
10C22×#4314—21no—
11C2×#66927C2211yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15#10622843—21no—
16C2×#66885—21no—
17C2×#66885—22no—
18#10622640—22no—
19#10622640—22no—
20#10622597—22no—
21#10622586—21no—
22C2×#66873—21no—
23#10622548C2211yescharacteristic
24#10622542—21no—
25#10622541—21no—
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622461—22no—
28#10622461—22no—
29C11×Q8⋊C8—22no—
30#10622094—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D44—21no—
33C22×D44—21no—
34C22×D44—21no—
35C22×Dic22D411yescharacteristic
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C42×C11—21no—
45C2×C42×C11C2311yescharacteristic
46C2×#4325—24no—
47C2×#4325—42no—
48C2×#4325—42no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C2×C4⋊Dic11D412yes—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—22no—
55C2×C4×Dic11—21no—
56C22×C11⋊C8—21no—
57C2×#4314—24no—
58C2×#4314—42no—
59C2×#4314—42no—
60#66927—21no—
61#66927—21no—
62#66927—21no—
63#66927D412yes—
64C4×Dic22—21no—
65C4×Dic22—21no—
66C4×Dic22—21no—
67C4×Dic22—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C4×C8×C11—21no—
71C4×C8×C11—21no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75#66885—24no—
76#66885—44no—
77#66873—24no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)D412yes—
80#10230—111nomaximal, Sylow
81C23×D11—41no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11SD1612yescomplemented
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—22no—
95C22×Dic11—21no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—42no—
100C2×D44—42no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—21no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×Dic22SD1612yescomplemented
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134#4325—48no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—42no—
138C4⋊Dic11—41no—
139C4⋊Dic11—41no—
140C4⋊Dic11—41no—
141C4⋊Dic11—41no—
142Dic11⋊C4—41no—
143Dic11⋊C4—41no—
144Dic11⋊C4—82no—
145C4×Dic11—41no—
146C4×Dic11—41no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—41no—
149C2×C11⋊C8—41no—
150#4314—48no—
151C2×#460—111no—
152C2×#460—111no—
153#2582—111no—
154#1957—111no—
155C2×Q8⋊C8—111no—
156C2×Q8⋊C8D1111yescharacteristic, complemented
157#1296—111no—
158C23×C11#12011yescharacteristic
159C22×D11—42no—
160C22×D11—81no—
161C22×D11—81no—
162C22×D11—81no—
163C22×D11—81no—
164C22×D11—81no—
165C22×D11—81no—
166Q8×C11—22no—
167Q8×C11—22no—
168Q8×C11—41no—
169Q8×C11—41no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12711yescharacteristic
184C2×C4×C11C2×SD1611yescharacteristic
185C2×C4×C11C2×SD1611yescharacteristic
186C2×C4×C11#13511yescharacteristic
187C2×C4×C11#13511yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11#13711yescharacteristic
191C2×C4×C11#13711yescharacteristic
192C2×Dic11—22no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201D44—44no—
202D44—42no—
203D44—42no—
204D44—42no—
205D44—42no—
206D44—82no—
207D44—81no—
208D44—81no—
209D44—81no—
210D44—81no—
211Dic22—22no—
212Dic22—22no—
213Dic22—41no—
214Dic22—41no—
215C8×C11—42no—
216C8×C11—42no—
217C11⋊C8—42no—
218C22×SD16—221no—
219C22×SD16—221no—
220C2×#127—111no—
221C2×C4×Q8—111no—
222C2×C4×Q8C2×D1111yescharacteristic
223#460—222no—
224#460—222no—
225#460—222no—
226#460—222no—
227C2×C4⋊C8—111no—
228C2×C4⋊C8C2×D1111yescharacteristic
229C2×#102—221no—
230C2×#102—221no—
231C2×#102—222no—
232C2×C4×C8C2×D1111yescharacteristic
233#398—222no—
234#391—221no—
235#391—221no—
236#389—221no—
237#389—221no—
238#384—111no—
239Q8⋊C8—22no—
240Q8⋊C8—222no—
241C22×C11#39211yescharacteristic
242C22×C11#44811yescharacteristic
243C22×C11#44811yescharacteristic
244C22×C11#44911yescharacteristic
245C22×C11#44911yescharacteristic
246C22×C11#45311yescharacteristic
247C22×C11#45411yescharacteristic
248C2×D11—82no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—161no—
252C2×D11—161no—
253C2×D11—161no—
254C2×D11—161no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—42no—
258C4×C11—81no—
259C4×C11#45011yescharacteristic
260C4×C11#45011yescharacteristic
261C4×C11#45211yescharacteristic
262C4×C11#45211yescharacteristic
263C4×C11#46511yescharacteristic
264C4×C11#46511yescharacteristic
265C4×C11#46811yescharacteristic
266C4×C11#46811yescharacteristic
267Dic11—42no—
268Dic11—82no—
269Dic11—81no—
270C22×Q8—111no—
271C22×Q8D4411yescharacteristic
272C22×D4—221no—
273C22×D4—221no—
274C22×D4—221no—
275C2×SD16—224no—
276C2×SD16—224no—
277C2×SD16—442no—
278C2×SD16—442no—
279C2×SD16—442no—
280C2×SD16—442no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—221no—
284#127—112no—
285#127—221no—
286#127—221no—
287#127—221no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—221no—
293C4×Q8—221no—
294C4×Q8—221no—
295C4×Q8—221no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4D4411yescharacteristic
304C2×C42—21no—
305C2×C42—221no—
306C2×C42C22×D1111yescharacteristic
307C4⋊C8—21no—
308C4⋊C8—112no—
309C4⋊C8—221no—
310C4⋊C8C22⋊D1112yes—
311#102—224no—
312#102—224no—
313#102—444no—
314C4×C8—21no—
315C4×C8—21no—
316#95—222no—
317#95—222no—
318#95—222no—
319C2×C11#162011yescharacteristic
320C2×C11#162311yescharacteristic
321C2×C11#162611yescharacteristic
322C2×C11#162611yescharacteristic
323C2×C11#200011yescharacteristic
324C2×C11#200011yescharacteristic
325C2×C11#200611yescharacteristic
326D11—162no—
327C24—441no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—112no—
334C2×Q8—221no—
335C2×Q8—221no—
336C2×Q8—221no—
337C2×Q8—221no—
338C2×Q8—221no—
339C2×Q8#431412yescomplemented
340C2×D4—222no—
341C2×D4—222no—
342C2×D4—222no—
343C2×D4—442no—
344C2×D4—442no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—441no—
355C2×D4—441no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—221no—
359C22×C4—222no—
360C22×C4—221no—
361C22×C4C2×D4411yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364SD16—448no—
365SD16—448no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—222no—
373C2×C8—441no—
374C2×C8—441no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—442no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—882no—
389C42—41no—
390C42—41no—
391C42—441no—
392C42—441no—
393C42#433911yescharacteristic
394C42D4×D1111yescharacteristic
395C42D4×D1111yescharacteristic
396C42C2×C22⋊D1111yescharacteristic
397C11#1023011yescharacteristic, complemented, Sylow
398C23—442no—
399C23—881no—
400C23—881no—
401C23—881no—
402C23—881no—
403C23—881no—
404C23—881no—
405C23#6693511yescharacteristic
406Q8—22no—
407Q8—22no—
408Q8—41no—
409Q8—41no—
410Q8—222no—
411Q8—222no—
412Q8—441no—
413Q8—441no—
414D4—444no—
415D4—442no—
416D4—442no—
417D4—442no—
418D4—442no—
419D4—882no—
420D4—881no—
421D4—881no—
422D4—881no—
423D4—881no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—222no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4#6693511yescharacteristic
442C2×C4#6693711yescharacteristic
443C2×C4#6693711yescharacteristic
444C2×C4C2×#431411yescharacteristic
445C2×C4#6695711yescharacteristic
446C2×C4#6696111yescharacteristic
447C2×C4#6696211yescharacteristic
448C2×C4SD16×D1111yescharacteristic
449C2×C4#6696711yescharacteristic
450C2×C4#6697111yescharacteristic
451C2×C4#6697211yescharacteristic
452C2×C4#6698311yescharacteristic
453C2×C4#6699011yescharacteristic
454C2×C4#6699311yescharacteristic
455C8—42no—
456C8—42no—
457C8—442no—
458C22—882no—
459C22—882no—
460C22—882no—
461C22—1761no—
462C22—1761no—
463C22—1761no—
464C22—1761no—
465C22#1062234711yescharacteristic
466C22#1062235111yescharacteristic
467C22#1062241911yescharacteristic
468C22#1062242411yescharacteristic
469C22#1062243511yescharacteristic
470C22#1062244011yescharacteristic
471C22#1062257311yescharacteristic
472C4—21no—
473C4—21no—
474C4—42no—
475C4—81no—
476C4—442no—
477C4—881no—
478C4—882no—
479C4#1062234411yescharacteristic
480C4#1062234611yescharacteristic
481C4#1062242011yescharacteristic
482C4#1062242511yescharacteristic
483C4#1062272711yescharacteristic
484C4#1062274711yescharacteristic
485C4#1062278211yescharacteristic
486C4#1062280011yescharacteristic
487C2—1762no—
488C2#1306767711yescharacteristic
489C2#1306769611yescharacteristic
490C2#1306771411yescharacteristic
491C2#1306771511yescharacteristic
492C2#1306961811yescharacteristic
493C2#1306962111yescharacteristic
494C2#1306965911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenterC2×Q8⋊C8D11
hypocenterC11#10230
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #13073986C2semidirect
5. C2×#10622094C2semidirect
6. #13066500C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
87. C2×Q8×C11SD16semidirect
117. C2×Dic22SD16semidirect
156. C2×Q8⋊C8D11semidirect
339. C2×Q8#4314semidirect
397. C11#10230semidirect

Maximal subgroups

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

subgroupindex
C2×#106224612
C2×#106226402
#130739862
#130694222
C2×#106220942
#130665002
C2×C11×Q8⋊C82
#1023011