Finite Group Databasebeta

← #14805620

Subgroups — #14805620

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×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic
4#13070107C212yesmaximal, complemented
5#13070001C212yesmaximal
6#13069578C211yesmaximal, characteristic, complemented
7#13069374C211yesmaximal, characteristic, complemented
8#13069346C212yesmaximal, complemented
9#13069298C212yesmaximal
10C4×#66873C211yesmaximal, characteristic
11C11×#2546C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66999—21no—
16C2×C4×D44C2211yescharacteristic
17C11×#398—22no—
18C11×#391—21no—
19C11×#389C2212yes—
20C11×#389C2212yes—
21C4×C11×C4⋊C4C2211yescharacteristic
22#10622700—24no—
23Q8×C11⋊C8—24no—
24#10622607—22no—
25#10622600—21no—
26C2×#66873C2212yes—
27C2×#66873C2211yescharacteristic
28C2×#66873C2211yescharacteristic
29C2×#66871C2212yes—
30C2×#66871C2212yes—
31#10622552C2212yes—
32#10622548C2211yescharacteristic
33#10622541C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37C2×C4×C11⋊C8C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—44no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2312yes—
62C2×C42×C11C2311yescharacteristic
63#66999—44no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—22no—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C4×D44—22no—
76C4×D44—22no—
77C11×#95—21no—
78C11×#95—22no—
79C11×#95—22no—
80C11⋊#95—22no—
81#66873—22no—
82#66873—24no—
83#66873Q814yescomplemented
84#66871—24no—
85#66871—24no—
86C4⋊(C11⋊C8)—24no—
87C4⋊(C11⋊C8)D414yes—
88C4×C11⋊C8—22no—
89C4×C11⋊C8—24no—
90#25469—111nomaximal, Sylow
91C23×D11—21no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11D814yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—21no—
107C22×Dic11—22no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44C2×Q812yes—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4—44no—
126C11×C4⋊C4C2×Q812yes—
127C11×C4⋊C4#4112yes—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11—42no—
131C42×C11C2×D412yes—
132C42×C11#4112yes—
133(C2×D11)⋊C4—42no—
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—82no—
136C4⋊Dic11—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—42no—
141C4⋊Dic11—81no—
142Dic11⋊C4—44no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C2×D414yes—
151C2×C11⋊C8C2×Q812yes—
152C2×#474—111no—
153C2×C8×Q8—111no—
154#2546D1111yescharacteristic, complemented
155#2538—111no—
156#2086—112no—
157#2067—112no—
158#1990—111no—
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—28no—
172Q8×C11—84no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11#12112yes—
190C2×C4×C11#12112yes—
191C2×C4×C11C2×D814yes—
192C2×C4×C11C2×D812yes—
193C2×C4×C11#13512yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11—42no—
206D44—22no—
207D44—22no—
208D44—41no—
209D44—41no—
210C4×D11—84no—
211C11⋊C8—24no—
212C11⋊C8—22no—
213C11⋊C8—41no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2×D1111yescharacteristic
216C2×C22⋊Q8—221no—
217C2×C4×Q8C2×D1111yescharacteristic
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×C8—111no—
230#398—22no—
231#396—222no—
232#391—21no—
233#390—112no—
234#389—112no—
235#389C2×D1112yes—
236#389C2×D1112yes—
237#384—111no—
238#380—221no—
239C4×C4⋊C4C2×D1111yescharacteristic
240#340—112no—
241#340—111no—
242#340—112no—
243#340—112no—
244#340—111no—
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—24no—
260C4×C11—22no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—82no—
265C4×C11#46614yes—
266C4×C11#53311yescharacteristic
267C4×C11#54111yescharacteristic
268C4×C11#54711yescharacteristic
269C4×C11D4×Q811yescharacteristic
270Dic11—82no—
271Dic11—81no—
272C22×Q8—21no—
273C22×Q8C22⋊D1111yescharacteristic
274C22×D4—111no—
275C23×C4—221no—
276C22×C8—111no—
277C22×C8—112no—
278C22×C8—111no—
279C4⋊Q8—22no—
280C4⋊Q8—22no—
281C4⋊Q8—44no—
282C22⋊Q8—444no—
283C4×Q8—22no—
284C4×Q8—22no—
285C4×D4—222no—
286C4×D4—222no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4C22⋊D1111yescharacteristic
296C2×C4⋊C4C22⋊D1112yes—
297C2×C4⋊C4C22×D1112yes—
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C4⋊C4C22×D1111yescharacteristic
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303C2×C42—21no—
304C2×C42C22×D1112yes—
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—224no—
314C4×C8—222no—
315#95—21no—
316#95—22no—
317#95—22no—
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—22no—
329C2×Q8—22no—
330C2×Q8—42no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×Q8#432314yes—
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—221no—
344C22×C4—222no—
345C22×C4—442no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4C2×C22⋊D1112yes—
349C22×C4C2×C22⋊D1112yes—
350C22×C4C2×C22⋊D1111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352C22×C4C23×D1111yescharacteristic
353C2×C8—114no—
354C2×C8—112no—
355C2×C8—221no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—221no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8—221no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—44no—
369C4⋊C4—44no—
370C4⋊C4—42no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—444no—
376C4⋊C4—442no—
377C4⋊C4—881no—
378C4⋊C4Q8×D1112yes—
379C4⋊C4#434312yes—
380C22⋊C4—444no—
381C22⋊C4—442no—
382C22⋊C4—882no—
383C42—22no—
384C42—22no—
385C42—42no—
386C42D4×D1112yes—
387C42#434112yes—
388C11#2546911yescharacteristic, complemented, Sylow
389C23—222no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23C22×C22⋊D1111yescharacteristic
397Q8—28no—
398Q8—84no—
399D4—222no—
400D4—222no—
401D4—441no—
402D4—441no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—442no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—442no—
425C2×C4—884no—
426C2×C4C2×#432314yes—
427C2×C4C2×#432312yes—
428C2×C4#6699212yes—
429C2×C4#6699212yes—
430C2×C4#6700312yes—
431C2×C4C2×D4×D1111yescharacteristic
432C2×C4C2×#434111yescharacteristic
433C2×C4C2×Q8×D1111yescharacteristic
434C2×C4C2×#434311yescharacteristic
435C2×C4#6704011yescharacteristic
436C2×C4#6704011yescharacteristic
437C8—224no—
438C8—222no—
439C8—441no—
440C22—442no—
441C22—442no—
442C22—442no—
443C22—881no—
444C22—881no—
445C22—881no—
446C22—881no—
447C22C22×#432311yescharacteristic
448C22C2×#6699211yescharacteristic
449C22Q8×C22⋊D1111yescharacteristic
450C22#1062334811yescharacteristic
451C22C2×#6700311yescharacteristic
452C22#1062336811yescharacteristic
453C22#1062336911yescharacteristic
454C4—22no—
455C4—24no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—82no—
460C4—882no—
461C4—881no—
462C4#1062265114yes—
463C4#1062325711yescharacteristic
464C4#1062325811yescharacteristic
465C4#1062325911yescharacteristic
466C4#1062326211yescharacteristic
467C2—882no—
468C2#1307221811yescharacteristic
469C2C2×#1062265111yescharacteristic
470C2#1307830311yescharacteristic
471C2#1308125111yescharacteristic
472C2#1308130111yescharacteristic
473C2Q8×#432311yescharacteristic
474C2#1308148711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2546C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2546D11
hypocenterC11#25469
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
4. #13070107C2semidirect
6. #13069578C2semidirect
7. #13069374C2semidirect
8. #13069346C2semidirect
11. C11×#2546C2semidirect
83. #66873Q8semidirect
154. #2546D11semidirect
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×Q8×C11⋊C82
#130735342
#130701072
#130700012
#130695782
#130693742
#130693462
#130692982
C4×#668732
C11×#25462
#2546911