Finite Group Databasebeta

← #14649939

Subgroups — #14649939

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622459C211yesmaximal, characteristic
2C2×C8×D44C211yesmaximal, characteristic
3#13069418C211yesmaximal, characteristic, complemented
4#13068617C211yesmaximal, characteristic
5C2×#10622124C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×C8×D11—21no—
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66885—21no—
15C2×#66885—21no—
16C2×(C2×D11)⋊C8—21no—
17C2×#66882—21no—
18C2×#66880—21no—
19C2×#66880—21no—
20#10622548C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22#10622459—22no—
23#10622459C414yescomplemented
24C8×D44—22no—
25C8×D44—22no—
26#10622189—21no—
27#10622124—22no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×Dic22—21no—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C22×C11⋊C8—21no—
44C2×C8×D11—24no—
45C2×C8×D11—42no—
46C2×C8×D11—42no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44C2×C412yes—
50C4×D44D412yes—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922C2×C412yes—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8C2×C412yes—
59C4×C8×C11—21no—
60C4×C8×C11—21no—
61#66885—24no—
62#66885—42no—
63(C2×D11)⋊C8—24no—
64#66882—24no—
65#66880—42no—
66#66880—42no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#9219—111nomaximal, Sylow
70C23×D11—21no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—41no—
76C22×Dic11—41no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44C22⋊C412yes—
81C2×D44SD1612yes—
82C2×D44Q1612yes—
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×Dic22—22no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×C8×C11—22no—
96C2×C8×C11—21no—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11D812yes—
107C42×C11C22×C411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11—21no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—81no—
123C4⋊Dic11C22⋊C412yes—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C8×D11—48no—
128C2×#474—111no—
129C2×C8×D4—111no—
130#1956—111no—
131#1802—111no—
132C2×#332—111no—
133#1296—111no—
134#1277D1111yescharacteristic, complemented
135C23×C11#12111yescharacteristic
136C22×D11—22no—
137C22×D11—22no—
138C22×D11—22no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11C2×C22⋊C411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11C2×Q1611yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×Dic11—22no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168D44—22no—
169D44—22no—
170D44—22no—
171D44#10314yescomplemented
172C4×D11—42no—
173C4×D11—42no—
174C4×D11—42no—
175C4×D11—42no—
176Dic22—42no—
177Dic22—42no—
178Dic22—81no—
179Dic22—81no—
180C8×C11—22no—
181C8×C11—42no—
182C8×C11—41no—
183C8×C11—81no—
184C11⋊C8—42no—
185C23×C8—221no—
186C2×C4⋊Q8—111no—
187C2×C4×D4—111no—
188#474—114no—
189#474—222no—
190C8×D4—222no—
191C8×D4—222no—
192C2×#107—221no—
193C2×C4⋊C8—111no—
194C2×C4⋊C8C2×D1111yescharacteristic
195C2×C4⋊C8C2×D1111yescharacteristic
196C2×#103—221no—
197C2×#103—221no—
198C2×#102—221no—
199C2×#102—221no—
200C2×C22⋊C8—221no—
201C2×C4×C8C2×D1111yescharacteristic
202#384—111no—
203#340—221no—
204#332—222no—
205C22×C11#38611yescharacteristic
206C22×C11#45911yescharacteristic
207C22×C11#46311yescharacteristic
208C22×C11#46511yescharacteristic
209C22×C11#46711yescharacteristic
210C22×C11#47111yescharacteristic
211C22×C11#47311yescharacteristic
212C2×D11—24no—
213C2×D11—42no—
214C2×D11—42no—
215C2×D11—42no—
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—42no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11C2×#10311yescharacteristic
222C4×C11#41611yescharacteristic
223C4×C11C4×D811yescharacteristic
224C4×C11#44211yescharacteristic
225C4×C11#44711yescharacteristic
226C4×C11#44911yescharacteristic
227C4×C11#46511yescharacteristic
228C4×C11#46711yescharacteristic
229Dic11—42no—
230Dic11—82no—
231Dic11—161no—
232C22×Q8—221no—
233C22×D4—111no—
234C23×C4—221no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—224no—
238C22×C8—221no—
239C22×C8—442no—
240C22×C8—442no—
241C22×C8D4411yescharacteristic
242C22×C8D4411yescharacteristic
243C4⋊Q8—112no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4×D4—112no—
248C4×D4—112no—
249C4×D4—221no—
250C4×D4—221no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C42C22×D1111yescharacteristic
259#107—224no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—112no—
264C4⋊C8—221no—
265C4⋊C8C4×D1112yes—
266#103—442no—
267#103—442no—
268#102—224no—
269#102—442no—
270C22⋊C8—224no—
271C4×C8—21no—
272C4×C8—21no—
273C2×C11#166511yescharacteristic
274C2×C11#166911yescharacteristic
275C2×C11#167911yescharacteristic
276C2×C11#168311yescharacteristic
277C2×C11#187911yescharacteristic
278C2×C11#189211yescharacteristic
279C2×C11#190811yescharacteristic
280D11—44no—
281C24—221no—
282C2×Q8—222no—
283C2×Q8—441no—
284C2×Q8—441no—
285C2×Q8—441no—
286C2×Q8—441no—
287C2×Q8—441no—
288C2×D4—112no—
289C2×D4—112no—
290C2×D4—112no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—221no—
294C22×C4—221no—
295C22×C4—222no—
296C22×C4—222no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4—441no—
302C22×C4—441no—
303C22×C4C2×D4411yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4#434311yescharacteristic
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—222no—
318C2×C8—448no—
319C2×C8—441no—
320C2×C8—441no—
321C2×C8D8812yes—
322C4⋊C4—112no—
323C4⋊C4—221no—
324C4⋊C4—222no—
325C4⋊C4—222no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C4⋊C4—881no—
333C22⋊C4—222no—
334C22⋊C4—222no—
335C42C2×C4×D1111yescharacteristic
336C42#433911yescharacteristic
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C11#921911yescharacteristic, complemented, Sylow
340C23—222no—
341C23—222no—
342C23—222no—
343C23—441no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23#6694811yescharacteristic
348Q8—442no—
349Q8—442no—
350Q8—881no—
351Q8—881no—
352D4—114no—
353D4—222no—
354D4—222no—
355D4—222no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—222no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—881no—
367C2×C4—881no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4—881no—
371C2×C4C4×D4411yescharacteristic
372C2×C4C22⋊C4×D1111yescharacteristic
373C2×C4#6693511yescharacteristic
374C2×C4#6693711yescharacteristic
375C2×C4#6694611yescharacteristic
376C2×C4#6694711yescharacteristic
377C2×C4C2×D8811yescharacteristic
378C2×C4#6695711yescharacteristic
379C2×C4#6696111yescharacteristic
380C2×C4#6696111yescharacteristic
381C2×C4#6696511yescharacteristic
382C2×C4SD16×D1111yescharacteristic
383C2×C4#6696911yescharacteristic
384C2×C4Q16×D1111yescharacteristic
385C8—22no—
386C8—41no—
387C8—42no—
388C8—81no—
389C8—442no—
390C22—224no—
391C22—442no—
392C22—442no—
393C22—442no—
394C22—442no—
395C22—442no—
396C22—442no—
397C22#1062227811yescharacteristic
398C22#1062245611yescharacteristic
399C22#1062245711yescharacteristic
400C22#1062247711yescharacteristic
401C22#1062250011yescharacteristic
402C22#1062250911yescharacteristic
403C22#1062251111yescharacteristic
404C4—21no—
405C4—21no—
406C4—442no—
407C4—882no—
408C4—1761no—
409C4C4×D8811yescharacteristic
410C4#1062232411yescharacteristic
411C4#1062234511yescharacteristic
412C4#1062234711yescharacteristic
413C4#1062238511yescharacteristic
414C4#1062239111yescharacteristic
415C4D11×#10311yescharacteristic
416C4#1062242611yescharacteristic
417C2—444no—
418C2#1306795811yescharacteristic
419C2#1306798211yescharacteristic
420C2#1306804011yescharacteristic
421C2#1306806811yescharacteristic
422C2#1306896311yescharacteristic
423C2#1306903811yescharacteristic
424C2#1306913011yescharacteristic
subgroupG/H
centerC23#66948
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socleC23×C11#121
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1277D11
hypocenterC11#9219
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
3. #13069418C2semidirect
5. C2×#10622124C2semidirect
6. #13066500C2semidirect
7. C11×#1277C2semidirect
23. #10622459C4semidirect
134. #1277D11semidirect
171. D44#103semidirect
339. C11#9219semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
C2×C8×D442
#130694182
#130686172
C2×#106221242
#130665002
C11×#12772
#921911