Finite Group Databasebeta

← #14805615

Subgroups — #14805615

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×#10622459C211yesmaximal, characteristic
2C2×#10622443C211yesmaximal, characteristic, complemented
3#13073604C211yesmaximal, characteristic, complemented
4#13073539C211yesmaximal, characteristic
5#13070106C212yesmaximal, complemented
6#13069999C212yesmaximal
7#13069576C211yesmaximal, characteristic, complemented
8#13069350C212yesmaximal, complemented
9#13069300C212yesmaximal
10C4×#66873C211yesmaximal, characteristic
11C11×#1947C211yesmaximal, characteristic, complemented
12C2×#66950—21no—
13C2×C4×D44C2211yescharacteristic
14C2×#66922—21no—
15C2×#66922C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×#107C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66885C2212yes—
22C2×#66882C2212yes—
23C2×Dic11⋊C8C2212yes—
24C2×C8×Dic11C2212yes—
25#10622607—22no—
26#10622601C2212yes—
27#10622600—21no—
28#10622598C2212yes—
29#10622598C2212yes—
30#10622598C2212yes—
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33#10622542—21no—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622459—24no—
36#10622443—24no—
37#10622274—22no—
38C11×#340C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22—21no—
46C22×Dic22D411yescharacteristic
47C22×C8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×Dic11⋊C4D412yes—
66C2×C4×Dic11C2312yes—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69#66950—44no—
70C4×D44—22no—
71C4×D44—22no—
72#66922—22no—
73#66922—22no—
74#66922—44no—
75C4×Dic22—22no—
76C4×Dic22—22no—
77C11×#107—24no—
78C11×C4⋊C8D414yes—
79C11×#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83#66885—24no—
84#66882—24no—
85Dic11⋊C8—24no—
86C8×Dic11—24no—
87#66873—22no—
88#66873Q814yescomplemented
89C4×C11⋊C8—22no—
90#25469—111nomaximal, Sylow
91C23×D11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—21no—
100C22×Dic11C2×D412yes—
101C22×Dic11C2×D412yes—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44C2×Q812yes—
108C2×C4×D11—42no—
109C2×C4×D11—42no—
110C2×C4×D11—42no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C2×Dic22—42no—
116C2×Dic22D814yes—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11C2×D414yes—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—81no—
126C11×C4⋊C4C2×Q812yes—
127C11×C4⋊C4#4112yes—
128C42×C11—42no—
129C42×C11C2×D412yes—
130C42×C11#4112yes—
131(C2×D11)⋊C4—44no—
132(C2×D11)⋊C4—42no—
133(C2×D11)⋊C4—82no—
134C4⋊Dic11—22no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—44no—
140C4⋊Dic11—44no—
141C4⋊Dic11—44no—
142C4⋊Dic11—42no—
143Dic11⋊C4—24no—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8C2×Q812yes—
152C2×#474—111no—
153C2×C8×Q8—111no—
154#2546—111no—
155#2538—111no—
156#2086—112no—
157#2067—112no—
158#1990—111no—
159#1947D1111yescharacteristic, complemented
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—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11#12112yes—
183C2×C4×C11#12112yes—
184C2×C4×C11C2×D812yes—
185C2×C4×C11#13512yes—
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×Q811yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C2×C4×C112−1+411yescharacteristic
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—42no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11C2×D814yes—
204D44—22no—
205D44—22no—
206D44—41no—
207D44—41no—
208C4×D11—84no—
209Dic22—28no—
210Dic22—84no—
211C8×C11—24no—
212C11⋊C8—22no—
213C11⋊C8—41no—
214C2×C4⋊Q8—111no—
215C2×C4⋊Q8—221no—
216C2×C22⋊Q8—221no—
217C2×C4×Q8—111no—
218C2×C4×D4—111no—
219#474—224no—
220C8×Q8—224no—
221C2×#107—112no—
222C2×#107C2×D1112yes—
223C2×C4⋊C8—112no—
224C2×C4⋊C8C2×D1111yescharacteristic
225C2×#102—111no—
226C2×#102—112no—
227C2×#102—111no—
228C2×C4×C8—112no—
229C2×C4×C8—111no—
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⋊C4C2×D1111yescharacteristic
240#340—112no—
241#340—111no—
242#340—112no—
243#340—111no—
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—42no—
261C4×C11—42no—
262C4×C11—82no—
263C4×C11#46614yes—
264C4×C11#53311yescharacteristic
265C4×C11#54111yescharacteristic
266C4×C11#54711yescharacteristic
267C4×C11D4×Q811yescharacteristic
268Dic11—24no—
269Dic11—42no—
270Dic11—82no—
271Dic11—81no—
272C22×Q8—111no—
273C22×Q8—221no—
274C22×D4—111no—
275C23×C4—221no—
276C22×C8—111no—
277C22×C8—111no—
278C22×C8C22×D1112yes—
279C4⋊Q8—222no—
280C4⋊Q8—222no—
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—111no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4C22×D1112yes—
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C4⋊C4C22×D1111yescharacteristic
300C2×C22⋊C4—222no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—222no—
303C2×C42—21no—
304C2×C42—112no—
305C2×C42C22×D1111yescharacteristic
306#107—24no—
307#107—224no—
308C4⋊C8—224no—
309C4⋊C8D4414yes—
310#102—114no—
311#102—224no—
312#102—222no—
313C4×C8—224no—
314C4×C8—222no—
315#95—21no—
316#95—222no—
317#95—222no—
318#95—222no—
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—114no—
329C2×Q8—222no—
330C2×Q8—222no—
331C2×Q8—442no—
332C2×Q8—442no—
333C2×Q8—442no—
334C2×D4—112no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—221no—
346C22×C4—222no—
347C22×C4—442no—
348C22×C4—442no—
349C22×C4—442no—
350C22×C4D4×D1111yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4C23×D1111yescharacteristic
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—112no—
356C2×C8—221no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8C2×D4414yes—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4—81no—
368C4⋊C4—224no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—222no—
374C4⋊C4—444no—
375C4⋊C4—444no—
376C4⋊C4—444no—
377C4⋊C4—442no—
378C4⋊C4#434112yes—
379C4⋊C4Q8×D1112yes—
380C22⋊C4—444no—
381C22⋊C4—442no—
382C22⋊C4—882no—
383C42—42no—
384C42—222no—
385C42—222no—
386C42C2×D4412yes—
387C42#434312yes—
388C11#2546911yescharacteristic, complemented, Sylow
389C23—222no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23C2×D4×D1111yescharacteristic
397Q8—228no—
398Q8—884no—
399D4—222no—
400D4—222no—
401D4—441no—
402D4—441no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—114no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4—441no—
423C2×C4—442no—
424C2×C4—441no—
425C2×C4—442no—
426C2×C4—884no—
427C2×C4#6694812yes—
428C2×C4#6694812yes—
429C2×C4D8×D1112yes—
430C2×C4#6697212yes—
431C2×C4C22×D4411yescharacteristic
432C2×C4C2×#434111yescharacteristic
433C2×C4C2×Q8×D1111yescharacteristic
434C2×C4C2×#434311yescharacteristic
435C2×C4#6704311yescharacteristic
436C2×C4#6704311yescharacteristic
437C8—24no—
438C8—222no—
439C8—441no—
440C22—442no—
441C22—442no—
442C22—442no—
443C22—881no—
444C22—881no—
445C22—881no—
446C22—881no—
447C22C2×#6694811yescharacteristic
448C22#1062312911yescharacteristic
449C22#1062316311yescharacteristic
450C22C2×D8×D1111yescharacteristic
451C22C2×#6697211yescharacteristic
452C22#1062330611yescharacteristic
453C22#1062331011yescharacteristic
454C4—22no—
455C4—42no—
456C4—42no—
457C4—82no—
458C4—224no—
459C4—442no—
460C4—881no—
461C4—882no—
462C4#1062249614yes—
463C4#1062308611yescharacteristic
464C4Q8×D4411yescharacteristic
465C4#1062322811yescharacteristic
466C4#1062325911yescharacteristic
467C2—882no—
468C2#1307221311yescharacteristic
469C2C2×#1062249611yescharacteristic
470C2#1307830811yescharacteristic
471C2#1308124611yescharacteristic
472C2#1308130511yescharacteristic
473C2#1308146611yescharacteristic
474C2#1308149011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1947D11
hypocenterC11#25469
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. C2×#10622443C2semidirect
3. #13073604C2semidirect
5. #13070106C2semidirect
7. #13069576C2semidirect
8. #13069350C2semidirect
11. C11×#1947C2semidirect
88. #66873Q8semidirect
159. #1947D11semidirect
388. C11#25469semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
C2×#106224432
#130736042
#130735392
#130701062
#130699992
#130695762
#130693502
#130693002
C4×#668732
C11×#19472
#2546911