Finite Group Databasebeta

← #14805618

Subgroups — #14805618

Order 2816.

838 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×#10622700C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13073605C211yesmaximal, characteristic, complemented
4#13073539C211yesmaximal, characteristic
5#13070108C212yesmaximal, complemented
6#13070005C212yesmaximal
7#13069372C211yesmaximal, characteristic, complemented
8#13069348C212yesmaximal, complemented
9#13069297C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66997—21no—
14C2×#66950—21no—
15C2×C4×D44C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18C11×#384C2211yescharacteristic
19#10622843—21no—
20C2×#66885C2211yescharacteristic
21C2×#66885C2211yescharacteristic
22C2×Dic11⋊C8C2212yes—
23C2×C8×Dic11C2212yes—
24#10622700—24no—
25#10622607—22no—
26#10622601C2212yes—
27#10622600—21no—
28#10622598C2212yes—
29#10622593—22no—
30#10622586C2212yes—
31#10622586C2212yes—
32C2×#66873C2212yes—
33C2×#66871C2212yes—
34C2×#66871C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C8×Dic22—24no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2211yescharacteristic
41#10622189C2211yescharacteristic
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11C2311yescharacteristic
57#66997—44no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4D412yes—
69C2×C4×Dic11—21no—
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8C2312yes—
72#66950—44no—
73C4×D44—22no—
74C4×D44—22no—
75C4×Dic22—22no—
76C4×Dic22—22no—
77C4×C8×C11—22no—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82#66885—22no—
83#66885Q814yescomplemented
84Dic11⋊C8—24no—
85C8×Dic11—24no—
86#66873—24no—
87#66871—24no—
88#66871—24no—
89C4⋊(C11⋊C8)D414yes—
90#25469—111nomaximal, Sylow
91C23×D11—21no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×Q8×C11—42no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D412yes—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44C2×Q812yes—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22D814yes—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11C2×Q812yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—81no—
130C42×C11C2×D412yes—
131C42×C11#4112yes—
132(C2×D11)⋊C4—44no—
133(C2×D11)⋊C4—42no—
134(C2×D11)⋊C4—82no—
135C4⋊Dic11—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—44no—
141C4⋊Dic11C2×Q812yes—
142C4⋊Dic11#4112yes—
143Dic11⋊C4—24no—
144Dic11⋊C4—44no—
145Dic11⋊C4—44no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—42no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8C2×D414yes—
152C2×#474—111no—
153C2×C8×Q8—111no—
154#2546—111no—
155#2538—111no—
156#2086—112no—
157#2067—112no—
158#1990D1111yescharacteristic, complemented
159#1947—111no—
160#1942—112no—
161#1934—112no—
162C4×#102—111no—
163C23×C11C22×D411yescharacteristic
164C22×D11—22no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171Q8×C11—84no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11#12112yes—
181C2×C4×C11#12112yes—
182C2×C4×C11C2×D812yes—
183C2×C4×C11#13512yes—
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×Q811yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11C2×D814yes—
205D44—22no—
206D44—22no—
207D44—41no—
208D44—41no—
209C4×D11—84no—
210Dic22—28no—
211C8×C11—22no—
212C8×C11—41no—
213C11⋊C8—24no—
214C2×C4⋊Q8—221no—
215C2×C4⋊Q8C2×D1111yescharacteristic
216C2×C22⋊Q8—221no—
217C2×C4×Q8—111no—
218C2×C4×D4—111no—
219#474—224no—
220C8×Q8—224no—
221C2×#107—112no—
222C2×#107—112no—
223C2×C4⋊C8—111no—
224C2×C4⋊C8—112no—
225C2×#102—111no—
226C2×#102—111no—
227C2×#102—112no—
228C2×C4×C8—112no—
229C2×C4×C8C2×D1111yescharacteristic
230#398—222no—
231#396—222no—
232#391—221no—
233#390—112no—
234#389—112no—
235#389—112no—
236#389—112no—
237#384C2×D1111yescharacteristic
238#380—221no—
239C4×C4⋊C4—111no—
240#340—111no—
241#340—111no—
242#340—112no—
243#340C2×D1112yes—
244#340C2×D1112yes—
245C22×C11C2×#12111yescharacteristic
246C22×C11#54811yescharacteristic
247C22×C11D4×Q811yescharacteristic
248C22×C11C22×D811yescharacteristic
249C22×C11C2×#13511yescharacteristic
250C22×C11#57711yescharacteristic
251C22×C11#57811yescharacteristic
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C4×C11—22no—
260C4×C11—82no—
261C4×C11—82no—
262C4×C11#46614yes—
263C4×C11#53311yescharacteristic
264C4×C11#54111yescharacteristic
265C4×C11#54711yescharacteristic
266C4×C11D4×Q811yescharacteristic
267Dic11—24no—
268Dic11—42no—
269Dic11—42no—
270Dic11—42no—
271Dic11—81no—
272C22×Q8—21no—
273C22×Q8—111no—
274C22×D4—111no—
275C23×C4—221no—
276C22×C8—112no—
277C22×C8C22×D1111yescharacteristic
278C22×C8C22×D1111yescharacteristic
279C4⋊Q8—22no—
280C4⋊Q8—22no—
281C4⋊Q8—444no—
282C22⋊Q8—444no—
283C4×Q8—222no—
284C4×Q8—222no—
285C4×D4—222no—
286C4×D4—222no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—112no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4C22×D1112yes—
299C2×C4⋊C4C22×D1112yes—
300C2×C22⋊C4—222no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—222no—
303C2×C42—112no—
304C2×C42—221no—
305C2×C42C22×D1111yescharacteristic
306#107—224no—
307#107—224no—
308C4⋊C8—114no—
309C4⋊C8—224no—
310#102—114no—
311#102—224no—
312#102—222no—
313C4×C8—22no—
314C4×C8—224no—
315#95—222no—
316#95—222no—
317#95—222no—
318#95—221no—
319C2×C11#242911yescharacteristic
320C2×C11C2×#46611yescharacteristic
321C2×C11#306311yescharacteristic
322C2×C11#335811yescharacteristic
323C2×C11#336411yescharacteristic
324C2×C11Q8×D811yescharacteristic
325C2×C11#338111yescharacteristic
326D11—82no—
327C24—221no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×Q8—114no—
332C2×Q8—222no—
333C2×Q8—222no—
334C2×D4—112no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—112no—
343C22×C4—112no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—442no—
348C22×C4—442no—
349C22×C4—442no—
350C22×C4D4×D1111yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4C23×D1111yescharacteristic
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—114no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8Q8×D1112yes—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—81no—
369C4⋊C4—112no—
370C4⋊C4—112no—
371C4⋊C4—224no—
372C4⋊C4—222no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—444no—
378C4⋊C4—444no—
379C4⋊C4—444no—
380C22⋊C4—444no—
381C22⋊C4—442no—
382C22⋊C4—882no—
383C42—222no—
384C42—222no—
385C42—442no—
386C42#433912yes—
387C42D4×D1112yes—
388C11#2546911yescharacteristic, complemented, Sylow
389C23—222no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23C2×D4×D1111yescharacteristic
397Q8—84no—
398Q8—228no—
399D4—222no—
400D4—222no—
401D4—441no—
402D4—441no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—114no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—884no—
427C2×C4#6693712yes—
428C2×C4#6693712yes—
429C2×C4D8×D1112yes—
430C2×C4#6696912yes—
431C2×C4C2×#433911yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C2×Q8×D1111yescharacteristic
434C2×C4#6704011yescharacteristic
435C2×C4#41×D1111yescharacteristic
436C2×C4#6704311yescharacteristic
437C8—22no—
438C8—41no—
439C8—224no—
440C22—442no—
441C22—442no—
442C22—442no—
443C22—881no—
444C22—881no—
445C22—881no—
446C22—881no—
447C22C2×#6693711yescharacteristic
448C22#1062320811yescharacteristic
449C22#1062325811yescharacteristic
450C22C2×D8×D1111yescharacteristic
451C22C2×#6696911yescharacteristic
452C22#1062329311yescharacteristic
453C22#1062329711yescharacteristic
454C4—22no—
455C4—82no—
456C4—82no—
457C4—224no—
458C4—442no—
459C4—442no—
460C4—442no—
461C4—881no—
462C4#1062238814yes—
463C4#1062310911yescharacteristic
464C4#1062311411yescharacteristic
465C4#1062316211yescharacteristic
466C4#1062316311yescharacteristic
467C2—882no—
468C2#1307221611yescharacteristic
469C2C2×#1062238811yescharacteristic
470C2#1307830511yescharacteristic
471C2#1308124811yescharacteristic
472C2#1308130611yescharacteristic
473C2#1308146811yescharacteristic
474C2#1308149611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1990D11
hypocenterC11#25469
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13073605C2semidirect
5. #13070108C2semidirect
7. #13069372C2semidirect
8. #13069348C2semidirect
11. C11×#1990C2semidirect
83. #66885Q8semidirect
158. #1990D11semidirect
388. C11#25469semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×C8×Dic222
#130736052
#130735392
#130701082
#130700052
#130693722
#130693482
#130692972
C4×#668852
C11×#19902
#2546911