Finite Group Databasebeta

← #14657314

Subgroups — #14657314

Order 2816.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073534C211yesmaximal, characteristic
2#13068744C211yesmaximal, characteristic, complemented
3#13068621C211yesmaximal, characteristic, complemented
4#13068617C211yesmaximal, characteristic
5C2×#10622097C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66999—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66899—21no—
14C2×#66885—21no—
15#10622607—22no—
16#10622600—21no—
17#10622552—21no—
18#10622548C2211yescharacteristic
19#10622548C2211yescharacteristic
20#10622541—21no—
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C11×Q8⋊C8—22no—
23#10622189—21no—
24#10622189—22no—
25#10622167—21no—
26#10622097—22no—
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40#66999—42no—
41#66999—42no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D412yes—
52C2×Dic11⋊C4—22no—
53C22×C11⋊C8—21no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62#66899—42no—
63C11⋊#95—22no—
64#66885—42no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67#10436—111nomaximal, Sylow
68C23×D11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11SD1612yes—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—22no—
82C22×Dic11—41no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44Q1612yes—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C42×C11—41no—
106C42×C11—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11#4111yescharacteristic
111(C2×D11)⋊C4—44no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—82no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127Dic11⋊C4—44no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#2538—111no—
132#1834—111no—
133#1803—111no—
134#1802—111no—
135C2×Q8⋊C8D1111yescharacteristic, complemented
136C2×D4⋊C8—111no—
137#1296—111no—
138C23×C11#12011yescharacteristic
139C22×D11—22no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146Q8×C11—22no—
147Q8×C11—22no—
148Q8×C11—41no—
149Q8×C11—41no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11#12311yescharacteristic
163C2×C4×C11#12411yescharacteristic
164C2×C4×C11C2×SD1611yescharacteristic
165C2×C4×C11C2×Q1611yescharacteristic
166C2×C4×C11#13511yescharacteristic
167C2×C4×C11#13511yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C11#13711yescharacteristic
172C2×Dic11—41no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181D44—22no—
182D44—22no—
183D44—41no—
184D44—41no—
185C4×D11—81no—
186C4×D11—81no—
187C4×D11—81no—
188C4×D11—81no—
189C8×C11—42no—
190C8×C11—81no—
191C11⋊C8—81no—
192C2×C22⋊Q8—221no—
193C2×C4×Q8C2×D1111yescharacteristic
194C2×C4×D4—111no—
195C2×C4⋊C8—111no—
196C2×C4⋊C8C2×D1111yescharacteristic
197C2×#103—221no—
198C2×#102—221no—
199C2×C4×C8C2×D1111yescharacteristic
200#396—222no—
201#390—221no—
202#389—221no—
203#384—111no—
204#384—111no—
205#380—221no—
206#340—221no—
207#340—222no—
208#340—221no—
209Q8⋊C8—22no—
210D4⋊C8—222no—
211C22×C11#39411yescharacteristic
212C22×C11#44911yescharacteristic
213C22×C11#44911yescharacteristic
214C22×C11#45011yescharacteristic
215C22×C11#45111yescharacteristic
216C22×C11#45411yescharacteristic
217C22×C11#45511yescharacteristic
218C2×D11—42no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11—81no—
229C4×C11#46511yescharacteristic
230C4×C11#46711yescharacteristic
231C4×C11#46811yescharacteristic
232C4×C11#46911yescharacteristic
233C4×C11#48111yescharacteristic
234C4×C11#48211yescharacteristic
235C4×C11#48411yescharacteristic
236C4×C11#48511yescharacteristic
237Dic11—82no—
238Dic11—81no—
239Dic11—161no—
240C22×Q8D4411yescharacteristic
241C22×D4—111no—
242C23×C4—221no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—221no—
246C22⋊Q8—442no—
247C22⋊Q8—442no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×D4—221no—
253C4×D4—221no—
254C4×D4—221no—
255C4×D4—221no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—222no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4D4411yescharacteristic
266C2×C22⋊C4—222no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—222no—
269C2×C42—21no—
270C2×C42C22×D1111yescharacteristic
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—221no—
274C4⋊C8—221no—
275#103—442no—
276#102—442no—
277C4×C8—21no—
278C4×C8C22⋊D1112yes—
279#95—222no—
280C2×C11#162811yescharacteristic
281C2×C11#163711yescharacteristic
282C2×C11#164211yescharacteristic
283C2×C11#164411yescharacteristic
284C2×C11#203411yescharacteristic
285C2×C11#203611yescharacteristic
286C2×C11#204011yescharacteristic
287D11—82no—
288C24—221no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8#431412yes—
295C2×D4—112no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—221no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—221no—
304C22×C4—222no—
305C22×C4—441no—
306C22×C4—441no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4C2×D4411yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8—441no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—442no—
331C4⋊C4—444no—
332C4⋊C4—442no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C22⋊C4—444no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—882no—
345C42—41no—
346C42—41no—
347C42#433911yescharacteristic
348C42#434111yescharacteristic
349C42#434111yescharacteristic
350C42C2×C22⋊D1111yescharacteristic
351C11#1043611yescharacteristic, complemented, Sylow
352C23—222no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23—441no—
359C23#6693511yescharacteristic
360Q8—22no—
361Q8—22no—
362Q8—41no—
363Q8—41no—
364D4—222no—
365D4—222no—
366D4—441no—
367D4—441no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—441no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—881no—
383C2×C4—881no—
384C2×C4—881no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4#6693611yescharacteristic
390C2×C4#6693811yescharacteristic
391C2×C4#6693911yescharacteristic
392C2×C4C2×#431411yescharacteristic
393C2×C4#6695711yescharacteristic
394C2×C4#6696111yescharacteristic
395C2×C4#6696111yescharacteristic
396C2×C4#6696711yescharacteristic
397C2×C4#6696811yescharacteristic
398C2×C4Q16×D1111yescharacteristic
399C2×C4#6697211yescharacteristic
400C2×C4#6698311yescharacteristic
401C2×C4#6699111yescharacteristic
402C2×C4#6699211yescharacteristic
403C8—42no—
404C8—81no—
405C8—881no—
406C22—442no—
407C22—442no—
408C22—442no—
409C22—881no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22#1062234411yescharacteristic
414C22#1062234711yescharacteristic
415C22#1062242111yescharacteristic
416C22#1062242411yescharacteristic
417C22#1062243811yescharacteristic
418C22#1062244011yescharacteristic
419C22#1062257411yescharacteristic
420C4—21no—
421C4—21no—
422C4—42no—
423C4—81no—
424C4—882no—
425C4—881no—
426C4—1761no—
427C4#1062234811yescharacteristic
428C4#1062235011yescharacteristic
429C4#1062242211yescharacteristic
430C4#1062242711yescharacteristic
431C4#1062272711yescharacteristic
432C4#1062274811yescharacteristic
433C4#1062278711yescharacteristic
434C4#1062280111yescharacteristic
435C2—882no—
436C2#1306772911yescharacteristic
437C2#1306778311yescharacteristic
438C2#1306781911yescharacteristic
439C2#1306783211yescharacteristic
440C2#1306980611yescharacteristic
441C2#1306981811yescharacteristic
442C2#1306984411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×Q8⋊C8D11
hypocenterC11#10436
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #13068744C2semidirect
3. #13068621C2semidirect
6. #13066500C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
135. C2×Q8⋊C8D11semidirect
351. C11#10436semidirect

Maximal subgroups

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

subgroupindex
#130735342
#130687442
#130686212
#130686172
C2×#106220972
#130665002
C2×C11×Q8⋊C82
#1043611