Finite Group Databasebeta

← #14656118

Subgroups — #14656118

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×#10622697C211yesmaximal, characteristic
2#13073534C211yesmaximal, characteristic
3#13069419C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#477C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66999—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#477—22no—
13C11×#477—22no—
14C2×C11×#107—21no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17C2×#66899—22no—
18#10622697—22no—
19#10622697—22no—
20#10622607—22no—
21#10622600—21no—
22C2×#66873—21no—
23C2×#66872—21no—
24#10622552—21no—
25#10622548C2211yescharacteristic
26#10622541—21no—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29Q8⋊(C11⋊C8)—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#66999—42no—
51#66999—42no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11D412yes—
59C2×Dic11⋊C4—22no—
60C22×C11⋊C8—21no—
61C22×C11⋊C8—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44—21no—
66C11×#107—24no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69C11×#103—24no—
70#66899—44no—
71C11⋊#95—22no—
72#66873—24no—
73#66872—24no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77C4×C11⋊C8—21no—
78#10236—111nomaximal, Sylow
79C23×D11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×Q8×C11—41no—
89C2×Q8×C11SD1612yes—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—22no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44Q1612yes—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C42×C11—41no—
122C42×C11—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127(C2×D11)⋊C4—44no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—82no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—42no—
134C4⋊Dic11—41no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138Dic11⋊C4—44no—
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×#477D1111yescharacteristic, complemented
146C2×#476—111no—
147#2538—111no—
148#1956—111no—
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—22no—
161Q8×C11—22no—
162Q8×C11—44no—
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—82no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12711yescharacteristic
183C2×C4×C11C2×SD1611yescharacteristic
184C2×C4×C11C2×Q1611yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11#13511yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11#13711yescharacteristic
189C2×C4×C11#13711yescharacteristic
190C2×C4×C11#13711yescharacteristic
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197D44—22no—
198D44—22no—
199D44—41no—
200D44—41no—
201C4×D11—81no—
202C4×D11—81no—
203C4×D11—81no—
204C4×D11—81no—
205C8×C11—42no—
206C11⋊C8—42no—
207C11⋊C8—42no—
208C2×C4⋊Q8C2×D1111yescharacteristic
209C2×C22⋊Q8—221no—
210C2×C4×Q8C2×D1111yescharacteristic
211C2×C4×D4—111no—
212#477—22no—
213#477—22no—
214#476—222no—
215#476—222no—
216C2×#107—21no—
217C2×#106—221no—
218C2×C4⋊C8—111no—
219C2×C4⋊C8C2×D1111yescharacteristic
220C2×#103—21no—
221C2×#103—222no—
222C2×#102—221no—
223C2×C4×C8—111no—
224#396—222no—
225#390—221no—
226#389—221no—
227#384—111no—
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—42no—
248C4×C11—81no—
249C4×C11—82no—
250C4×C11#44811yescharacteristic
251C4×C11#44911yescharacteristic
252C4×C11#45111yescharacteristic
253C4×C11#45211yescharacteristic
254C4×C11#46511yescharacteristic
255C4×C11#46711yescharacteristic
256C4×C11#46811yescharacteristic
257C4×C11#47011yescharacteristic
258Dic11—82no—
259Dic11—81no—
260C22×Q8—21no—
261C22×Q8C22⋊D1111yescharacteristic
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⋊Q8C22⋊D1112yes—
271C22⋊Q8—442no—
272C22⋊Q8—442no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×Q8—21no—
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—111no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4C22⋊D1111yescharacteristic
290C2×C22⋊C4—222no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—222no—
293C2×C42—21no—
294C2×C42C22×D1111yescharacteristic
295#107—24no—
296#106—224no—
297C4⋊C8—21no—
298C4⋊C8—112no—
299C4⋊C8—221no—
300C4⋊C8C22⋊D1112yes—
301#103—24no—
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—21no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×Q8—41no—
325C2×Q8#432512yes—
326C2×D4—112no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—41no—
335C22×C4—221no—
336C22×C4—222no—
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—21no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—442no—
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—41no—
376C42—41no—
377C42D4×D1111yescharacteristic
378C42#434111yescharacteristic
379C42C2×C22⋊D1111yescharacteristic
380C42C2×C22⋊D1111yescharacteristic
381C11#1023611yescharacteristic, complemented, Sylow
382C23—222no—
383C23—441no—
384C23—441no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23—441no—
389C23#6699011yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—44no—
393Q8—41no—
394Q8—41no—
395Q8—82no—
396D4—222no—
397D4—222no—
398D4—441no—
399D4—441no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—441no—
414C2×C4—442no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—881no—
418C2×C4—881no—
419C2×C4—881no—
420C2×C4—881no—
421C2×C4Q16×D1111yescharacteristic
422C2×C4#6697111yescharacteristic
423C2×C4#6697111yescharacteristic
424C2×C4#6697211yescharacteristic
425C2×C4#6699011yescharacteristic
426C2×C4#6699111yescharacteristic
427C2×C4#6699211yescharacteristic
428C2×C4#6699211yescharacteristic
429C2×C4#6699311yescharacteristic
430C2×C4C2×#432511yescharacteristic
431C2×C4#6699511yescharacteristic
432C2×C4#6700211yescharacteristic
433C2×C4#6700311yescharacteristic
434C2×C4#6700611yescharacteristic
435C8—42no—
436C8—442no—
437C8—442no—
438C22—442no—
439C22—442no—
440C22—442no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22#1062265911yescharacteristic
446C22#1062266011yescharacteristic
447C22#1062279911yescharacteristic
448C22#1062280011yescharacteristic
449C22#1062281111yescharacteristic
450C22#1062281411yescharacteristic
451C22#1062283611yescharacteristic
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—82no—
457C4—881no—
458C4—882no—
459C4#1062266111yescharacteristic
460C4#1062266211yescharacteristic
461C4#1062279911yescharacteristic
462C4#1062280011yescharacteristic
463C4#1062280111yescharacteristic
464C4#1062280211yescharacteristic
465C4#1062284011yescharacteristic
466C4#1062285111yescharacteristic
467C2—882no—
468C2#1306774111yescharacteristic
469C2#1306774911yescharacteristic
470C2#1306777911yescharacteristic
471C2#1306778711yescharacteristic
472C2#1306961711yescharacteristic
473C2#1306962311yescharacteristic
474C2#1306965611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#477C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#477D11
hypocenterC11#10236
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13069419C2semidirect
4. C2×Q8⋊(C11⋊C8)C2semidirect
6. #13066500C2semidirect
7. C2×C11×#477C2semidirect
145. C2×#477D11semidirect
381. C11#10236semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
#130735342
#130694192
C2×Q8⋊(C11⋊C8)2
C2×#106221212
#130665002
C2×C11×#4772
#1023611