Finite Group Databasebeta

← #14656105

Subgroups — #14656105

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×#10622459C211yesmaximal, characteristic
2C2×#10622462C211yesmaximal, characteristic, complemented
3#13073539C211yesmaximal, characteristic
4#13069576C211yesmaximal, characteristic, complemented
5C2×#10622122C211yesmaximal, characteristic, complemented
6C2×#10622121C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic, complemented
8C22×Dic44—21no—
9C2×#66950—21no—
10C2×C4×D44C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C11×#384C2211yescharacteristic
16C2×#66885—21no—
17C2×#66882—21no—
18C2×#66880—21no—
19#10622607—22no—
20#10622601—21no—
21#10622600—21no—
22#10622598—21no—
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622462—22no—
25#10622462—22no—
26#10622459—22no—
27#10622459—22no—
28#10622167—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—
52C2×Dic44—24no—
53C2×Dic44—42no—
54C2×Dic44—42no—
55#66950—42no—
56#66950—42no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922D412yes—
65C4×Dic22—21no—
66C4×Dic22—21no—
67C4×Dic22—21no—
68C4×Dic22—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yes—
72C11×C4⋊C8D412yes—
73C11⋊#95—22no—
74#66885—24no—
75#66882—24no—
76#66880—24no—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10233—111nomaximal, Sylow
80C23×D11—21no—
81C22×C4×C11—22no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—41no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44Q1612yescomplemented
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×Dic22—21no—
102C2×Dic22—22no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22—21no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22—41no—
112C2×Dic22D812yes—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128(C2×D11)⋊C4—44no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—82no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—44no—
139C4⋊Dic11—41no—
140C4⋊Dic11—41no—
141Dic11⋊C4—41no—
142Dic11⋊C4—41no—
143C4×Dic11—41no—
144C4×Dic11—41no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148Dic44—48no—
149C2×#474—111no—
150C2×#462—111no—
151#2538—111no—
152#1990—111no—
153C2×Q8⋊C8—111no—
154C2×D4⋊C8—111no—
155#1296D1111yescharacteristic, complemented
156C23×C11#12011yescharacteristic
157C22×D11—22no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12711yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C2×Q1611yescharacteristic
177C2×C4×C11#13511yescharacteristic
178C2×C4×C11#13511yescharacteristic
179C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C11#13711yescharacteristic
182C2×C4×C11#13711yescharacteristic
183C2×Dic11—22no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—81no—
194C2×Dic11—81no—
195D44—22no—
196D44—22no—
197D44—41no—
198D44—41no—
199C4×D11—81no—
200C4×D11—81no—
201C4×D11—81no—
202C4×D11—81no—
203Dic22—22no—
204Dic22—22no—
205Dic22—41no—
206Dic22—41no—
207Dic22—42no—
208Dic22—42no—
209Dic22—81no—
210Dic22—81no—
211C8×C11—42no—
212C8×C11—42no—
213C11⋊C8—42no—
214C22×Q16—221no—
215C2×C4⋊Q8—111no—
216C2×C22⋊Q8—221no—
217C2×C4×Q8—111no—
218C2×C4×D4—111no—
219#474—222no—
220#474—222no—
221#462—222no—
222#462—222no—
223C2×#107—221no—
224C2×C4⋊C8C2×D1111yescharacteristic
225C2×C4⋊C8C2×D1111yescharacteristic
226C2×#103—221no—
227C2×#102—221no—
228C2×C4×C8—111no—
229#396—222no—
230#390—221no—
231#389—221no—
232#384C2×D1111yescharacteristic
233#380—221no—
234#340—222no—
235Q8⋊C8—222no—
236D4⋊C8—222no—
237C22×C11#39211yescharacteristic
238C22×C11#44711yescharacteristic
239C22×C11#44911yescharacteristic
240C22×C11#45111yescharacteristic
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#44711yescharacteristic
255C4×C11#44911yescharacteristic
256C4×C11#45111yescharacteristic
257C4×C11#45211yescharacteristic
258C4×C11#46611yescharacteristic
259C4×C11#46711yescharacteristic
260C4×C11#46911yescharacteristic
261C4×C11#47011yescharacteristic
262Dic11—42no—
263Dic11—82no—
264Dic11—81no—
265Dic11—81no—
266C22×Q8—111no—
267C22×Q8—221no—
268C22×D4—111no—
269C23×C4—221no—
270C2×Q16—224no—
271C2×Q16—442no—
272C2×Q16—442no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—221no—
276C4⋊Q8—112no—
277C4⋊Q8—221no—
278C4⋊Q8—221no—
279C4⋊Q8—221no—
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—111no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4D4412yes—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C42—221no—
303C2×C42C22×D1111yescharacteristic
304#107—224no—
305C4⋊C8—21no—
306C4⋊C8—21no—
307C4⋊C8D4412yes—
308C4⋊C8D4412yes—
309#103—224no—
310#102—224no—
311C4×C8—221no—
312C4×C8—221no—
313#95—222no—
314C2×C11#164111yescharacteristic
315C2×C11#164411yescharacteristic
316C2×C11#164911yescharacteristic
317C2×C11#165211yescharacteristic
318C2×C11#199911yescharacteristic
319C2×C11#200111yescharacteristic
320C2×C11#200711yescharacteristic
321D11—82no—
322C24—221no—
323C2×Q8—112no—
324C2×Q8—221no—
325C2×Q8—221no—
326C2×Q8—222no—
327C2×Q8—221no—
328C2×Q8—221no—
329C2×Q8—221no—
330C2×Q8—441no—
331C2×Q8—441no—
332C2×Q8—441no—
333C2×Q8—441no—
334C2×Q8—441no—
335C2×D4—112no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—221no—
341C22×C4—22no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4C2×D4411yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4D4×D1111yescharacteristic
355Q16—448no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—222no—
363C2×C8—441no—
364C2×C8—441no—
365C4⋊C4—42no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—222no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—222no—
376C4⋊C4—444no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C22⋊C4—444no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—882no—
385C42—441no—
386C42—441no—
387C42C2×D4411yescharacteristic
388C42C2×D4411yescharacteristic
389C42D4×D1111yescharacteristic
390C42#434311yescharacteristic
391C11#1023311yescharacteristic, complemented, Sylow
392C23—222no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23#6693511yescharacteristic
400Q8—222no—
401Q8—222no—
402Q8—441no—
403Q8—441no—
404Q8—442no—
405Q8—442no—
406Q8—881no—
407Q8—881no—
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—222no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—881no—
428C2×C4—881no—
429C2×C4—881no—
430C2×C4—881no—
431C2×C4—881no—
432C2×C4—881no—
433C2×C4#6692711yescharacteristic
434C2×C4#6693511yescharacteristic
435C2×C4#6693511yescharacteristic
436C2×C4#6694811yescharacteristic
437C2×C4#6694811yescharacteristic
438C2×C4#6694811yescharacteristic
439C2×C4D8×D1111yescharacteristic
440C2×C4#6696511yescharacteristic
441C2×C4#6696711yescharacteristic
442C2×C4#6696711yescharacteristic
443C2×C4#6696811yescharacteristic
444C2×C4#6696811yescharacteristic
445C2×C4Q16×D1111yescharacteristic
446C2×C4#6697211yescharacteristic
447C8—42no—
448C8—42no—
449C8—442no—
450C22—442no—
451C22—442no—
452C22—442no—
453C22—881no—
454C22—881no—
455C22—881no—
456C22—881no—
457C22#1062228411yescharacteristic
458C22#1062235911yescharacteristic
459C22#1062236511yescharacteristic
460C22#1062238611yescharacteristic
461C22#1062239611yescharacteristic
462C22#1062242111yescharacteristic
463C22#1062242411yescharacteristic
464C4—21no—
465C4—21no—
466C4—82no—
467C4—442no—
468C4—881no—
469C4—882no—
470C4—881no—
471C4#1062238611yescharacteristic
472C4#1062239611yescharacteristic
473C4#1062242111yescharacteristic
474C4#1062242411yescharacteristic
475C4#1062247811yescharacteristic
476C4#1062248111yescharacteristic
477C4#1062249611yescharacteristic
478C4#1062250011yescharacteristic
479C2—882no—
480C2#1306781011yescharacteristic
481C2#1306783111yescharacteristic
482C2#1306786611yescharacteristic
483C2#1306788711yescharacteristic
484C2#1306961511yescharacteristic
485C2#1306962711yescharacteristic
486C2#1306966511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1296D11
hypocenterC11#10233
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
2. C2×#10622462C2semidirect
4. #13069576C2semidirect
5. C2×#10622122C2semidirect
7. C11×#1296C2semidirect
94. C2×D44Q16semidirect
155. #1296D11semidirect
391. C11#10233semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
C2×#106224622
#130735392
#130695762
C2×#106221222
C2×#106221212
C11×#12962
#1023311