Finite Group Databasebeta

← #14780100

Subgroups — #14780100

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66983C211yesmaximal, characteristic
2#13069412C212yesmaximal, complemented
3#13069230C212yesmaximal, complemented
4#13069179C212yesmaximal, complemented
5#13068912C212yesmaximal, complemented
6#13068910C212yesmaximal, complemented
7#13068800C212yesmaximal, complemented
8#13068596C211yesmaximal, characteristic, complemented
9C11×#1817C211yesmaximal, characteristic, complemented
10C22×C42×C11C2211yescharacteristic
11C2×#66983C411yescharacteristic
12C2×C4×C22⋊D11C2212yes—
13C22×#4313C2212yes—
14C2×C4×D44C2211yescharacteristic
15C2×C11×C22⋊C8C2212yes—
16#10622826C412yes—
17#10622825C411yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20C2×(C2×D11)⋊C8C2212yes—
21C2×(C2×D11)⋊C8C2212yes—
22C2×(C2×D11)⋊C8C2212yes—
23C2×#66879C2212yes—
24C2×Dic11⋊C8C2212yes—
25#10622553C412yes—
26#10622552C411yescharacteristic
27C4×(C2×D11)⋊C4C2212yes—
28C4×C4⋊Dic11C2211yescharacteristic
29#10622541C411yescharacteristic
30C2×C4⋊(C11⋊C8)C2212yes—
31C11×#336C2211yescharacteristic
32C11×#336C2212yes—
33C11×#336C2211yescharacteristic
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2212yes—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C412yes—
41C22×D44C2×C411yescharacteristic
42C22×C4×D11C2312yes—
43C22×C8×C11C2312yes—
44C22×C8×C11C2312yes—
45C2×C42×C11—42no—
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C22⋊Dic11C2×C412yes—
51#66983—24no—
52C4×C22⋊D11—42no—
53C4×C22⋊D11—42no—
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×(C2×D11)⋊C4C2×C412yes—
56C2×(C2×D11)⋊C4C2×C412yes—
57C2×(C2×D11)⋊C4C2×C412yes—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×C4⋊Dic11C2×C411yescharacteristic
61C2×Dic11⋊C4C2×C412yes—
62C2×C4×Dic11C2312yes—
63C22×C11⋊C8C2312yes—
64C22×C11⋊C8C2312yes—
65C2×#4313—42no—
66C2×#4313—42no—
67C2×#4313—42no—
68C4×D44—42no—
69C11×C22⋊C8—42no—
70C11⋊#95C2×C412yes—
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73C22⋊(C11⋊C8)—41no—
74C22⋊(C11⋊C8)—41no—
75(C2×D11)⋊C8—42no—
76(C2×D11)⋊C8—42no—
77(C2×D11)⋊C8—42no—
78#66879—42no—
79Dic11⋊C8—42no—
80C4⋊(C11⋊C8)—42no—
81#23334—111nomaximal, Sylow
82C24×C11C22×C411yescharacteristic
83C23×D11C22×C412yes—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11M1614yescomplemented
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C2×C22⋊D11—24no—
101C2×C22⋊D11—42no—
102C2×C22⋊D11—42no—
103C22×Dic11C22×C412yes—
104C22×Dic11C22×C412yes—
105C22×Dic11C22×C412yes—
106C2×D44—22no—
107C2×D44—41no—
108C2×D44—41no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C42×C11—22no—
122C42×C11—22no—
123C42×C11—41no—
124C42×C11—41no—
125C22⋊Dic11—42no—
126(C2×D11)⋊C4—24no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—42no—
130C4⋊Dic11—22no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133Dic11⋊C4—42no—
134C4×Dic11—22no—
135C4×Dic11—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142#4313—48no—
143C4×#121—111no—
144#1955—112no—
145#1924—112no—
146#1917—112no—
147#1870—112no—
148#1870—112no—
149#1851—112no—
150#1817D1111yescharacteristic, complemented
151#1797—111no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11C2×M1612yes—
159C23×C11C23×C411yescharacteristic
160C22×D11—22no—
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—22no—
164C22×D11—22no—
165C22×D11—22no—
166C22×D11—22no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—44no—
181C2×C4×C11—44no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11C2×M1612yes—
185C2×C4×C11C2×M1612yes—
186C2×C4×C11H(5,𝔽2)12yes—
187C2×C4×C11H(5,𝔽2)11yescharacteristic
188C2×C4×C11H(5,𝔽2)12yes—
189C2×C4×C112−1+411yescharacteristic
190C22⋊D11—48no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200D44—44no—
201C4×D11—42no—
202C4×D11—42no—
203C4×D11—42no—
204C4×D11—42no—
205C8×C11—42no—
206C8×C11—42no—
207C11⋊C8—42no—
208C11⋊C8—42no—
209C22×M16—112no—
210C2×#121—111no—
211C2×C4×D4—112no—
212C2×C4×D4—111no—
213C22×C42C2×D1111yescharacteristic
214C2×C4⋊C8—112no—
215C2×C4⋊C8—112no—
216C2×C22⋊C8—111no—
217C2×C22⋊C8—111no—
218C2×C22⋊C8—112no—
219C2×C22⋊C8—112no—
220C2×C22⋊C8—112no—
221C2×C22⋊C8C2×D1112yes—
222C2×#97—112no—
223#390—111no—
224#389—111no—
225#388—112no—
226#386—112no—
227#380—111no—
228C4×C4⋊C4—111no—
229C4×C22⋊C4—112no—
230#336—112no—
231#336—112no—
232#336—112no—
233#336C2×D1111yescharacteristic
234#336C2×D1112yes—
235#336C2×D1111yescharacteristic
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11#51811yescharacteristic
244C22×C11#51811yescharacteristic
245C22×C11#52011yescharacteristic
246C22×C11C22×M1611yescharacteristic
247C22×C11#56811yescharacteristic
248C22×C11#56811yescharacteristic
249C22×C11#56811yescharacteristic
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—42no—
256C2×D11—42no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—41no—
260C4×C11—41no—
261C4×C11—41no—
262C4×C11#56012yes—
263C4×C11#56212yes—
264Dic11—42no—
265Dic11—42no—
266Dic11—42no—
267C22×D4—112no—
268C22×D4—111no—
269C23×C4—112no—
270C23×C4C4×D1111yescharacteristic
271C23×C4C4×D1111yescharacteristic
272C23×C4C22×D1111yescharacteristic
273C2×M16—442no—
274C2×M16—442no—
275C2×M16—442no—
276C22×C8—112no—
277C22×C8—112no—
278C22×C8C22×D1112yes—
279C22×C8C22×D1112yes—
280#121—224no—
281C4×D4—442no—
282C4×D4—442no—
283C4×D4—442no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—111no—
288C2×C22⋊C4—112no—
289C2×C22⋊C4—112no—
290C2×C22⋊C4—112no—
291C2×C22⋊C4—112no—
292C2×C22⋊C4—112no—
293C2×C42—42no—
294C2×C42—112no—
295C2×C42C4×D1111yescharacteristic
296C2×C42C4×D1111yescharacteristic
297C2×C42C22×D1111yescharacteristic
298C2×C42C22×D1111yescharacteristic
299C4⋊C8—442no—
300C4⋊C8—442no—
301C22⋊C8—42no—
302C22⋊C8—442no—
303C22⋊C8—442no—
304C22⋊C8—442no—
305C22⋊C8—441no—
306C22⋊C8—441no—
307#97—442no—
308#95—112no—
309#95—112no—
310#95—112no—
311C2×C11—42no—
312C2×C11#237711yescharacteristic
313C2×C11#297311yescharacteristic
314C2×C11#297511yescharacteristic
315C2×C11#297811yescharacteristic
316C2×C11#298011yescharacteristic
317C2×C11#298911yescharacteristic
318C2×C11#299511yescharacteristic
319D11—82no—
320C24—112no—
321C24C2×C4×D1111yescharacteristic
322C2×D4—224no—
323C2×D4—222no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4—442no—
327C2×D4—442no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—112no—
338C22×C4—112no—
339C22×C4—112no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4#431314yescomplemented
347C22×C4C2×C4×D1111yescharacteristic
348C22×C4C2×C4×D1111yescharacteristic
349C22×C4C2×C4×D1111yescharacteristic
350C22×C4C2×C4×D1111yescharacteristic
351C22×C4C2×C4×D1111yescharacteristic
352C22×C4C23×D1111yescharacteristic
353M16—448no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—222no—
366C4⋊C4—222no—
367C4⋊C4—442no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C22⋊C4—224no—
371C22⋊C4—442no—
372C22⋊C4—442no—
373C22⋊C4—442no—
374C22⋊C4—442no—
375C42—22no—
376C42—22no—
377C42—41no—
378C42—41no—
379C42—222no—
380C42—222no—
381C11#2333411yescharacteristic, complemented, Sylow
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—222no—
389C23—222no—
390C23—222no—
391C23—222no—
392C23—222no—
393C23—222no—
394C23—222no—
395C23C2×#431312yes—
396C23C22×C4×D1111yescharacteristic
397D4—444no—
398D4—448no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4C2×#431312yes—
430C2×C4C2×#431312yes—
431C2×C4#6703712yes—
432C2×C4#6704211yescharacteristic
433C2×C4#6704212yes—
434C2×C4#6704311yescharacteristic
435C8—42no—
436C8—42no—
437C8—442no—
438C8—442no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—442no—
447C22—442no—
448C22—442no—
449C22—442no—
450C22—442no—
451C22—442no—
452C22—442no—
453C22#1062301711yescharacteristic
454C22#1062305211yescharacteristic
455C22#1062305411yescharacteristic
456C22C22×#431311yescharacteristic
457C22#1062327611yescharacteristic
458C22#1062327611yescharacteristic
459C22#1062327611yescharacteristic
460C4—22no—
461C4—22no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—442no—
466C4—442no—
467C4—442no—
468C4#1062319712yes—
469C4#1062319812yes—
470C2—42no—
471C2—882no—
472C2#1307177511yescharacteristic
473C2#1307764211yescharacteristic
474C2#1307765611yescharacteristic
475C2#1307767611yescharacteristic
476C2#1307768611yescharacteristic
477C2#1307772911yescharacteristic
478C2#1307778811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1817C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1817D11
hypocenterC11#23334
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #13069412C2semidirect
3. #13069230C2semidirect
4. #13069179C2semidirect
5. #13068912C2semidirect
6. #13068910C2semidirect
7. #13068800C2semidirect
8. #13068596C2semidirect
9. C11×#1817C2semidirect
93. C22×C4×C11M16semidirect
150. #1817D11semidirect
346. C22×C4#4313semidirect
381. C11#23334semidirect

Maximal subgroups

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

subgroupindex
C4×#669832
#130694122
#130692302
#130691792
#130689122
#130689102
#130688002
#130685962
C11×#18172
#2333411