Finite Group Databasebeta

← #14656124

Subgroups — #14656124

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622463C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic
3#13073539C211yesmaximal, characteristic
4#13069417C211yesmaximal, characteristic, complemented
5C2×#10622122C211yesmaximal, characteristic, complemented
6C2×#10622121C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×#66950—21no—
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C11×#384C2211yescharacteristic
15C2×#66885—21no—
16C2×#66882—21no—
17C2×#66881—21no—
18C2×#66880—21no—
19#10622607—22no—
20#10622601—21no—
21#10622600—21no—
22#10622598—21no—
23C2×#66874—22no—
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622463—22no—
26#10622463—22no—
27#10622455—22no—
28#10622455—22no—
29#10622122—22no—
30#10622121—22no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22—21no—
34C22×Dic22D411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D412yes—
40C2×C42×C11C2311yescharacteristic
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—22no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C22×C11⋊C8—21no—
52#66950—42no—
53#66950—42no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C4×Dic22—21no—
63C4×Dic22—21no—
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69C11×C4⋊C8D412yes—
70C11⋊#95—22no—
71#66885—24no—
72#66882—24no—
73#66881—24no—
74#66880—24no—
75#66874—44no—
76C4×C11⋊C8—21no—
77C4×C11⋊C8—21no—
78#10236—111nomaximal, Sylow
79C23×D11—21no—
80C22×C4×C11—22no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—41no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44Q1612yes—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22—22no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22—42no—
107C2×Dic22—42no—
108C2×Dic22—41no—
109C2×Dic22SD1612yes—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125(C2×D11)⋊C4—44no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—82no—
129C4⋊Dic11—22no—
130C4⋊Dic11—21no—
131C4⋊Dic11—22no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—44no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140C4×Dic11—41no—
141C4×Dic11—41no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×#477—111no—
146C2×#476—111no—
147#2538—111no—
148#1956—111no—
149C2×Q8⋊C8—111no—
150C2×D4⋊C8—111no—
151#1296D1111yescharacteristic, complemented
152C23×C11#12011yescharacteristic
153C22×D11—22no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12711yescharacteristic
171C2×C4×C11C2×SD1611yescharacteristic
172C2×C4×C11C2×Q1611yescharacteristic
173C2×C4×C11#13511yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C2×C4×C11#13711yescharacteristic
178C2×C4×C11#13711yescharacteristic
179C2×Dic11—22no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191D44—22no—
192D44—22no—
193D44—41no—
194D44—41no—
195C4×D11—81no—
196C4×D11—81no—
197C4×D11—81no—
198C4×D11—81no—
199Dic22—22no—
200Dic22—22no—
201Dic22—41no—
202Dic22—41no—
203Dic22—44no—
204Dic22—82no—
205C8×C11—42no—
206C8×C11—42no—
207C11⋊C8—42no—
208C2×C4⋊Q8—111no—
209C2×C22⋊Q8—221no—
210C2×C4×Q8—111no—
211C2×C4×D4—111no—
212#477—222no—
213#477—222no—
214#476—222no—
215#476—222no—
216C2×#107—221no—
217C2×#106—221no—
218C2×C4⋊C8C2×D1111yescharacteristic
219C2×C4⋊C8C2×D1111yescharacteristic
220C2×#103—221no—
221C2×#103—222no—
222C2×#102—221no—
223C2×C4×C8—111no—
224#396—222no—
225#390—221no—
226#389—221no—
227#384C2×D1111yescharacteristic
228#380—221no—
229Q8⋊C8—222no—
230D4⋊C8—222no—
231C22×C11#39211yescharacteristic
232C22×C11#45011yescharacteristic
233C22×C11#45111yescharacteristic
234C22×C11#45211yescharacteristic
235C22×C11#45211yescharacteristic
236C22×C11#45311yescharacteristic
237C22×C11#45411yescharacteristic
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—42no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—82no—
248C4×C11#44811yescharacteristic
249C4×C11#44911yescharacteristic
250C4×C11#45111yescharacteristic
251C4×C11#45211yescharacteristic
252C4×C11#46511yescharacteristic
253C4×C11#46711yescharacteristic
254C4×C11#46811yescharacteristic
255C4×C11#47011yescharacteristic
256Dic11—42no—
257Dic11—81no—
258Dic11—82no—
259Dic11—81no—
260C22×Q8—111no—
261C22×Q8—221no—
262C22×D4—111no—
263C23×C4—221no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—221no—
267C4⋊Q8—112no—
268C4⋊Q8—221no—
269C4⋊Q8—221no—
270C4⋊Q8—221no—
271C22⋊Q8—442no—
272C22⋊Q8—442no—
273C4×Q8—221no—
274C4×Q8—221no—
275C4×Q8—221no—
276C4×Q8—221no—
277C4×D4—221no—
278C4×D4—221no—
279C4×D4—221no—
280C4×D4—221no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4D4412yes—
290C2×C22⋊C4—222no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—222no—
293C2×C42—221no—
294C2×C42C22×D1111yescharacteristic
295#107—224no—
296#106—224no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8D4412yes—
300C4⋊C8D4412yes—
301#103—224no—
302#103—444no—
303#102—224no—
304C4×C8—221no—
305C4×C8—221no—
306#95—222no—
307C2×C11#163111yescharacteristic
308C2×C11#163211yescharacteristic
309C2×C11#163711yescharacteristic
310C2×C11#163811yescharacteristic
311C2×C11#200011yescharacteristic
312C2×C11#200111yescharacteristic
313C2×C11#200611yescharacteristic
314D11—82no—
315C24—221no—
316C2×Q8—112no—
317C2×Q8—221no—
318C2×Q8—221no—
319C2×Q8—221no—
320C2×Q8—222no—
321C2×Q8—221no—
322C2×Q8—221no—
323C2×Q8—442no—
324C2×Q8—442no—
325C2×Q8—441no—
326C2×D4—112no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C22×C4—22no—
333C22×C4—221no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—441no—
337C22×C4—441no—
338C22×C4—441no—
339C22×C4—441no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4C2×D4411yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C22×C4D4×D1111yescharacteristic
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—222no—
353C2×C8—441no—
354C2×C8—441no—
355C4⋊C4—42no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—222no—
361C4⋊C4—222no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—444no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C22⋊C4—444no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C22⋊C4—882no—
375C42—441no—
376C42—441no—
377C42C2×D4411yescharacteristic
378C42C2×D4411yescharacteristic
379C42D4×D1111yescharacteristic
380C42#434311yescharacteristic
381C11#1023611yescharacteristic, complemented, Sylow
382C23—222no—
383C23—441no—
384C23—441no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23—441no—
389C23#6693511yescharacteristic
390Q8—222no—
391Q8—222no—
392Q8—444no—
393Q8—441no—
394Q8—441no—
395Q8—882no—
396D4—222no—
397D4—222no—
398D4—441no—
399D4—441no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—222no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—442no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—881no—
416C2×C4—881no—
417C2×C4—881no—
418C2×C4—881no—
419C2×C4—881no—
420C2×C4—881no—
421C2×C4#6692711yescharacteristic
422C2×C4#6693511yescharacteristic
423C2×C4#6693511yescharacteristic
424C2×C4#6694811yescharacteristic
425C2×C4#6694811yescharacteristic
426C2×C4#6694811yescharacteristic
427C2×C4#6696411yescharacteristic
428C2×C4#6696511yescharacteristic
429C2×C4SD16×D1111yescharacteristic
430C2×C4#6696811yescharacteristic
431C2×C4#6696811yescharacteristic
432C2×C4#6696911yescharacteristic
433C2×C4Q16×D1111yescharacteristic
434C2×C4#6697111yescharacteristic
435C8—42no—
436C8—42no—
437C8—442no—
438C22—442no—
439C22—442no—
440C22—442no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22#1062228411yescharacteristic
446C22#1062236011yescharacteristic
447C22#1062236611yescharacteristic
448C22#1062238911yescharacteristic
449C22#1062239611yescharacteristic
450C22#1062242111yescharacteristic
451C22#1062242311yescharacteristic
452C4—21no—
453C4—21no—
454C4—82no—
455C4—442no—
456C4—881no—
457C4—881no—
458C4—882no—
459C4#1062239411yescharacteristic
460C4#1062239611yescharacteristic
461C4#1062241911yescharacteristic
462C4#1062242111yescharacteristic
463C4#1062247711yescharacteristic
464C4#1062248111yescharacteristic
465C4#1062249911yescharacteristic
466C4#1062250011yescharacteristic
467C2—882no—
468C2#1306774411yescharacteristic
469C2#1306775111yescharacteristic
470C2#1306778211yescharacteristic
471C2#1306778911yescharacteristic
472C2#1306962211yescharacteristic
473C2#1306962711yescharacteristic
474C2#1306966011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1296D11
hypocenterC11#10236
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. C2×#10622463C2semidirect
4. #13069417C2semidirect
5. C2×#10622122C2semidirect
7. C11×#1296C2semidirect
151. #1296D11semidirect
381. C11#10236semidirect

Maximal subgroups

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

subgroupindex
C2×#106224632
C2×#106224552
#130735392
#130694172
C2×#106221222
C2×#106221212
C11×#12962
#1023611