Finite Group Databasebeta

← #14656094

Subgroups — #14656094

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622707C211yesmaximal, characteristic, complemented
2C2×#10622696C211yesmaximal, characteristic
3#13073539C211yesmaximal, characteristic
4C2×#10622094C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4325—21no—
10C2×#66950—21no—
11C2×C4×D44C2211yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C11×#384C2211yescharacteristic
15C2×#66899—21no—
16#10622707—22no—
17#10622707—22no—
18#10622696—22no—
19#10622696—22no—
20#10622607—22no—
21#10622601—21no—
22#10622600—21no—
23#10622598—21no—
24C2×#66874—21no—
25C2×#66872—21no—
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C11×#340—22no—
29#10622097—22no—
30#10622094—22no—
31C22×Q8×C11—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22D411yescharacteristic
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×#4325—24no—
47C2×#4325—42no—
48C2×#4325—42no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D411yescharacteristic
55C2×Dic11⋊C4—21no—
56C2×C4×Dic11—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59#66950—42no—
60#66950—42no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65C4×Dic22—21no—
66C4×Dic22—21no—
67C4×Dic22—21no—
68C4×Dic22—21no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71#66899—24no—
72C11⋊#95—22no—
73#66874—24no—
74#66872—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78C4⋊(C11⋊C8)D412yes—
79#10232—111nomaximal, Sylow
80C23×D11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C22×C4×C11—22no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44SD1612yes—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22—21no—
110C2×Dic22—21no—
111C2×Dic22—21no—
112C2×Dic22SD1612yescomplemented
113C2×C8×C11—22no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129#4325—48no—
130(C2×D11)⋊C4—44no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—82no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—44no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141C4×Dic11—41no—
142C4×Dic11—41no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149C2×#475—111no—
150C2×#461—111no—
151#2538—111no—
152#1990D1111yescharacteristic, complemented
153C2×Q8⋊C8—111no—
154C2×D4⋊C8—111no—
155#1296—111no—
156C23×C11#12011yescharacteristic
157C22×D11—22no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164Q8×C11—42no—
165Q8×C11—42no—
166Q8×C11—81no—
167Q8×C11—81no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12711yescharacteristic
182C2×C4×C11C2×SD1611yescharacteristic
183C2×C4×C11C2×SD1611yescharacteristic
184C2×C4×C11#13511yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11#13711yescharacteristic
189C2×C4×C11#13711yescharacteristic
190C2×Dic11—22no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199D44—22no—
200D44—22no—
201D44—41no—
202D44—41no—
203C4×D11—81no—
204C4×D11—81no—
205C4×D11—81no—
206C4×D11—81no—
207Dic22—22no—
208Dic22—22no—
209Dic22—41no—
210Dic22—41no—
211C8×C11—42no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C22×SD16—221no—
215C2×C4⋊Q8C2×D1111yescharacteristic
216C2×C22⋊Q8—221no—
217C2×C4×Q8—111no—
218C2×C4×D4—111no—
219#475—222no—
220#475—222no—
221#461—222no—
222#461—222no—
223C2×#106—221no—
224C2×C4⋊C8—111no—
225C2×C4⋊C8—111no—
226C2×#103—221no—
227C2×#103—221no—
228C2×C4×C8C2×D1111yescharacteristic
229#396—222no—
230#390—221no—
231#389—221no—
232#384C2×D1111yescharacteristic
233#380—221no—
234#340—22no—
235Q8⋊C8—222no—
236D4⋊C8—222no—
237C22×C11#39211yescharacteristic
238C22×C11#44811yescharacteristic
239C22×C11#44911yescharacteristic
240C22×C11#45011yescharacteristic
241C22×C11#45211yescharacteristic
242C22×C11#45511yescharacteristic
243C22×C11#45611yescharacteristic
244C2×D11—42no—
245C2×D11—42no—
246C2×D11—42no—
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—81no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—82no—
254C4×C11—82no—
255C4×C11#44811yescharacteristic
256C4×C11#44911yescharacteristic
257C4×C11#45011yescharacteristic
258C4×C11#45211yescharacteristic
259C4×C11#46511yescharacteristic
260C4×C11#46511yescharacteristic
261C4×C11#46811yescharacteristic
262C4×C11#46811yescharacteristic
263Dic11—42no—
264Dic11—81no—
265Dic11—81no—
266C22×Q8—21no—
267C22×Q8—111no—
268C22×D4—111no—
269C23×C4—221no—
270C2×SD16—224no—
271C2×SD16—442no—
272C2×SD16—442no—
273C22×C8—21no—
274C22×C8—221no—
275C22×C8—221no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8D4412yes—
280C22⋊Q8—442no—
281C22⋊Q8—442no—
282C4×Q8—221no—
283C4×Q8—221no—
284C4×Q8—221no—
285C4×Q8—221no—
286C4×D4—221no—
287C4×D4—221no—
288C4×D4—221no—
289C4×D4—221no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4C22⋊D1112yes—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C42—221no—
303C2×C42C22×D1111yescharacteristic
304#106—224no—
305C4⋊C8—112no—
306C4⋊C8—112no—
307C4⋊C8—221no—
308C4⋊C8—221no—
309#103—224no—
310#103—224no—
311C4×C8—21no—
312C4×C8—21no—
313#95—222no—
314C2×C11#164211yescharacteristic
315C2×C11#164311yescharacteristic
316C2×C11#165011yescharacteristic
317C2×C11#165111yescharacteristic
318C2×C11#200011yescharacteristic
319C2×C11#200011yescharacteristic
320C2×C11#200711yescharacteristic
321D11—82no—
322C24—221no—
323C2×Q8—22no—
324C2×Q8—41no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8—112no—
330C2×Q8—221no—
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—221no—
334C2×Q8—221no—
335C2×D4—112no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—221no—
341C22×C4—22no—
342C22×C4—41no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4C2×C22⋊D1111yescharacteristic
355SD16—448no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—441no—
362C2×C8—441no—
363C2×C8—441no—
364C2×C8—441no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—444no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C22⋊C4—444no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—882no—
385C42—441no—
386C42—441no—
387C42C2×D4411yescharacteristic
388C42#433911yescharacteristic
389C42D4×D1111yescharacteristic
390C42D4×D1111yescharacteristic
391C11#1023211yescharacteristic, complemented, Sylow
392C23—222no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23#6699011yescharacteristic
400Q8—42no—
401Q8—42no—
402Q8—81no—
403Q8—81no—
404Q8—222no—
405Q8—222no—
406Q8—441no—
407Q8—441no—
408D4—222no—
409D4—222no—
410D4—441no—
411D4—441no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—222no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—881no—
430C2×C4—881no—
431C2×C4—881no—
432C2×C4—881no—
433C2×C4#6693511yescharacteristic
434C2×C4#6693511yescharacteristic
435C2×C4#6693711yescharacteristic
436C2×C4#6693711yescharacteristic
437C2×C4#6696411yescharacteristic
438C2×C4#6696511yescharacteristic
439C2×C4SD16×D1111yescharacteristic
440C2×C4SD16×D1111yescharacteristic
441C2×C4#6696711yescharacteristic
442C2×C4#6696811yescharacteristic
443C2×C4#6697111yescharacteristic
444C2×C4#6697211yescharacteristic
445C2×C4#6698311yescharacteristic
446C2×C4#6699311yescharacteristic
447C8—42no—
448C8—442no—
449C8—442no—
450C22—442no—
451C22—442no—
452C22—442no—
453C22—881no—
454C22—881no—
455C22—881no—
456C22—881no—
457C22#1062257311yescharacteristic
458C22#1062267411yescharacteristic
459C22#1062270811yescharacteristic
460C22#1062277111yescharacteristic
461C22#1062278211yescharacteristic
462C22#1062278311yescharacteristic
463C22#1062280011yescharacteristic
464C4—21no—
465C4—21no—
466C4—82no—
467C4—82no—
468C4—442no—
469C4—881no—
470C4—881no—
471C4#1062238911yescharacteristic
472C4#1062239111yescharacteristic
473C4#1062239311yescharacteristic
474C4#1062239611yescharacteristic
475C4#1062241911yescharacteristic
476C4#1062242011yescharacteristic
477C4#1062242411yescharacteristic
478C4#1062242511yescharacteristic
479C2—882no—
480C2#1306781311yescharacteristic
481C2#1306782011yescharacteristic
482C2#1306786911yescharacteristic
483C2#1306787611yescharacteristic
484C2#1306961811yescharacteristic
485C2#1306962011yescharacteristic
486C2#1306966211yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1990C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1990D11
hypocenterC11#10232
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#10622707C2semidirect
4. C2×#10622094C2semidirect
6. #13066499C2semidirect
7. C11×#1990C2semidirect
112. C2×Dic22SD16semidirect
152. #1990D11semidirect
391. C11#10232semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
C2×#106226962
#130735392
C2×#106220942
C2×#106220972
#130664992
C11×#19902
#1023211