Finite Group Databasebeta

← #14656120

Subgroups — #14656120

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×#10622704C211yesmaximal, characteristic, complemented
2C2×#10622697C211yesmaximal, characteristic
3#13073539C211yesmaximal, characteristic
4C2×#10622094C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1956C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66950—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C2×C11×#103—22no—
13C2×C4×C8×C11C2211yescharacteristic
14C11×#384C2211yescharacteristic
15#10622704—22no—
16#10622704—22no—
17#10622697—22no—
18#10622697—22no—
19#10622607—22no—
20#10622601—21no—
21#10622600—21no—
22#10622598—21no—
23C2×#66874—21no—
24C2×#66873—21no—
25C2×#66872—21no—
26C2×#66871—21no—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
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×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×C4×Dic11—21no—
54C22×C11⋊C8—21no—
55C22×C11⋊C8—21no—
56#66950—42no—
57#66950—42no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—21no—
62C4×Dic22—21no—
63C4×Dic22—21no—
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×#103—44no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C11⋊#95—22no—
70#66874—24no—
71#66873—24no—
72#66872—24no—
73#66871—24no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4⋊(C11⋊C8)D412yes—
78#10236—111nomaximal, Sylow
79C23×D11—21no—
80C2×Q8×C11—22no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×Q8×C11—41no—
84C22×C4×C11—22no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44Q1612yes—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22—21no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22SD1612yes—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126(C2×D11)⋊C4—44no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—82no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—44no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C4×Dic11—41no—
138C4×Dic11—41no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×#477—111no—
146C2×#476—111no—
147#2538—111no—
148#1956D1111yescharacteristic, complemented
149C2×Q8⋊C8—111no—
150C2×D4⋊C8—111no—
151#1296—111no—
152C23×C11#12011yescharacteristic
153C22×D11—22no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160Q8×C11—44no—
161Q8×C11—82no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12711yescharacteristic
176C2×C4×C11C2×SD1611yescharacteristic
177C2×C4×C11C2×Q1611yescharacteristic
178C2×C4×C11#13511yescharacteristic
179C2×C4×C11#13511yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C11#13711yescharacteristic
182C2×C4×C11#13711yescharacteristic
183C2×C4×C11#13711yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193D44—22no—
194D44—22no—
195D44—41no—
196D44—41no—
197C4×D11—81no—
198C4×D11—81no—
199C4×D11—81no—
200C4×D11—81no—
201Dic22—22no—
202Dic22—22no—
203Dic22—41no—
204Dic22—41no—
205C8×C11—42no—
206C11⋊C8—42no—
207C11⋊C8—42no—
208C2×C4⋊Q8C2×D1111yescharacteristic
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⋊C8—111no—
219C2×C4⋊C8—111no—
220C2×#103—22no—
221C2×#103—221no—
222C2×#102—221no—
223C2×C4×C8C2×D1111yescharacteristic
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—82no—
249C4×C11#44811yescharacteristic
250C4×C11#44911yescharacteristic
251C4×C11#45111yescharacteristic
252C4×C11#45211yescharacteristic
253C4×C11#46511yescharacteristic
254C4×C11#46711yescharacteristic
255C4×C11#46811yescharacteristic
256C4×C11#47011yescharacteristic
257Dic11—42no—
258Dic11—81no—
259Dic11—81no—
260C22×Q8—21no—
261C22×Q8—111no—
262C22×D4—111no—
263C23×C4—221no—
264C22×C8—21no—
265C22×C8—221no—
266C22×C8—221no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8D4412yes—
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—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4C22⋊D1112yes—
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—112no—
298C4⋊C8—112no—
299C4⋊C8—221no—
300C4⋊C8—221no—
301#103—44no—
302#103—224no—
303#102—224no—
304C4×C8—21no—
305C4×C8—21no—
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—22no—
317C2×Q8—42no—
318C2×Q8—42no—
319C2×Q8—41no—
320C2×Q8—112no—
321C2×Q8—221no—
322C2×Q8—221no—
323C2×Q8—221no—
324C2×Q8—221no—
325C2×Q8—221no—
326C2×D4—112no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—221no—
337C22×C4—441no—
338C22×C4—441no—
339C22×C4—441no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4D4×D1111yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C22×C4C2×C22⋊D1111yescharacteristic
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—222no—
350C2×C8—222no—
351C2×C8—441no—
352C2×C8—441no—
353C2×C8—441no—
354C2×C8—441no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—42no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—444no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C22⋊C4—444no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C22⋊C4—882no—
375C42—441no—
376C42—441no—
377C42C2×D4411yescharacteristic
378C42#433911yescharacteristic
379C42D4×D1111yescharacteristic
380C42D4×D1111yescharacteristic
381C11#1023611yescharacteristic, complemented, Sylow
382C23—222no—
383C23—441no—
384C23—441no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23—441no—
389C23#6699011yescharacteristic
390Q8—44no—
391Q8—82no—
392Q8—222no—
393Q8—222no—
394Q8—441no—
395Q8—441no—
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—42no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—222no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—881no—
418C2×C4—881no—
419C2×C4—881no—
420C2×C4—881no—
421C2×C4#6693511yescharacteristic
422C2×C4#6693511yescharacteristic
423C2×C4#6693711yescharacteristic
424C2×C4#6693711yescharacteristic
425C2×C4SD16×D1111yescharacteristic
426C2×C4#6696711yescharacteristic
427C2×C4#6696811yescharacteristic
428C2×C4#6696911yescharacteristic
429C2×C4Q16×D1111yescharacteristic
430C2×C4#6697111yescharacteristic
431C2×C4#6697111yescharacteristic
432C2×C4#6697211yescharacteristic
433C2×C4#6698311yescharacteristic
434C2×C4#6699311yescharacteristic
435C8—42no—
436C8—442no—
437C8—442no—
438C22—442no—
439C22—442no—
440C22—442no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22#1062257311yescharacteristic
446C22#1062267511yescharacteristic
447C22#1062269011yescharacteristic
448C22#1062278211yescharacteristic
449C22#1062278611yescharacteristic
450C22#1062279911yescharacteristic
451C22#1062280011yescharacteristic
452C4—21no—
453C4—21no—
454C4—82no—
455C4—82no—
456C4—442no—
457C4—881no—
458C4—881no—
459C4#1062241911yescharacteristic
460C4#1062242011yescharacteristic
461C4#1062242111yescharacteristic
462C4#1062242311yescharacteristic
463C4#1062242411yescharacteristic
464C4#1062242511yescharacteristic
465C4#1062242611yescharacteristic
466C4#1062242911yescharacteristic
467C2—882no—
468C2#1306774011yescharacteristic
469C2#1306774711yescharacteristic
470C2#1306777811yescharacteristic
471C2#1306778511yescharacteristic
472C2#1306961811yescharacteristic
473C2#1306962511yescharacteristic
474C2#1306965711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1956C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1956D11
hypocenterC11#10236
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
1. C2×#10622704C2semidirect
4. C2×#10622094C2semidirect
6. #13066499C2semidirect
7. C11×#1956C2semidirect
148. #1956D11semidirect
381. C11#10236semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
C2×#106226972
#130735392
C2×#106220942
C2×#106220972
#130664992
C11×#19562
#1023611