Finite Group Databasebeta

← #14812741

Subgroups — #14812741

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071563C211yesmaximal, characteristic
2#13070140C212yesmaximal
3#13070001C212yesmaximal
4#13069382C212yesmaximal, complemented
5#13069379C211yesmaximal, characteristic, complemented
6#13069335C211yesmaximal, characteristic, complemented
7#13069205C212yesmaximal, complemented
8#13068775C211yesmaximal, characteristic, complemented
9#13068613C211yesmaximal, characteristic
10C4×#66873C211yesmaximal, characteristic
11C11×#2571C211yesmaximal, characteristic, complemented
12C2×#66945—21no—
13C2×C4×D44C2211yescharacteristic
14C11×#400—22no—
15C11×#389—21no—
16C11×#389C2212yes—
17C11×#384C2211yescharacteristic
18C11×#382—21no—
19C11×#382C2212yes—
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22#10622600—21no—
23C2×#66873C2211yescharacteristic
24C2×#66873C2211yescharacteristic
25C2×#66873C2212yes—
26C2×#66872C2212yes—
27C2×#66871C2212yes—
28C2×#66871C2212yes—
29#10622552C2212yes—
30#10622548C2211yescharacteristic
31C4×C4⋊Dic11C2212yes—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622283—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2211yescharacteristic
39#10622167C2211yescharacteristic
40#10622162C2212yes—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4×Dic11—22no—
62C22×C11⋊C8C2312yes—
63C22×C11⋊C8C2311yescharacteristic
64C22×C11⋊C8C2311yescharacteristic
65#66945—44no—
66C4×D44—22no—
67C4×D44Q814yes—
68C11×#95—21no—
69C11×#95—22no—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95D412yes—
73C11⋊#95—22no—
74#66873—22no—
75#66873—22no—
76#66873—42no—
77#66872—42no—
78#66871—24no—
79#66871—42no—
80C4⋊(C11⋊C8)—22no—
81C4⋊(C11⋊C8)—24no—
82C4×C11⋊C8—22no—
83#26087—111nomaximal, Sylow
84C23×D11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2411yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—22no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44C2×Q812yes—
101C2×C4×D11—24no—
102C2×C4×D11—42no—
103C2×C4×D11—42no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—81no—
114C11×C4⋊C4—82no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—42no—
118C42×C11C2×Q812yes—
119C42×C11#4112yes—
120(C2×D11)⋊C4—24no—
121(C2×D11)⋊C4—44no—
122(C2×D11)⋊C4—82no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—42no—
127C4⋊Dic11—81no—
128C4⋊Dic11C2×Q812yes—
129C4×Dic11—44no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8#4112yes—
138C2×C11⋊C8#4112yes—
139#2571D1111yescharacteristic, complemented
140#2354—111no—
141#2092—112no—
142#2067—112no—
143#1949—112no—
144#1948—111no—
145#1939—111no—
146#1921—112no—
147#1845—111no—
148#1802—111no—
149C4×#102—111no—
150C23×C11C22×D411yescharacteristic
151C22×D11—22no—
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11C22⋊Q812yes—
176C2×C4×C11C22⋊Q812yes—
177C2×C4×C11#13512yes—
178C2×C4×C11AGL(1,ℤ/8)12yes—
179C2×C4×C11C22×Q811yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11H(5,𝔽2)11yescharacteristic
184C2×C4×C112−1+411yescharacteristic
185C2×Dic11—22no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191D44—22no—
192D44—22no—
193D44—41no—
194D44—41no—
195C4×D11—48no—
196C11⋊C8—22no—
197C11⋊C8—22no—
198C11⋊C8—42no—
199C2×C4×D4—111no—
200C2×#117—221no—
201C2×#107—112no—
202C2×#107—112no—
203C2×#106—112no—
204C2×C4⋊C8—111no—
205C2×C4⋊C8—112no—
206C2×#102—111no—
207C2×#102—111no—
208C2×#102—112no—
209C2×C4×C8—111no—
210#400—22no—
211#390—112no—
212#389—21no—
213#389C2×D1112yes—
214#388—222no—
215#384—111no—
216#384C2×D1111yescharacteristic
217#382—21no—
218#382C2×D1112yes—
219#380—221no—
220C4×C4⋊C4—112no—
221C4×C4⋊C4C2×D1111yescharacteristic
222C4×C4⋊C4C2×D1111yescharacteristic
223#340—112no—
224#340—112no—
225#340—111no—
226#340—111no—
227#336—112no—
228C22×C11C2×C22⋊Q811yescharacteristic
229C22×C11#54711yescharacteristic
230C22×C11#55011yescharacteristic
231C22×C11C2×#13511yescharacteristic
232C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C22×C11#57611yescharacteristic
234C22×C11#57811yescharacteristic
235C2×D11—42no—
236C2×D11—42no—
237C2×D11—42no—
238C2×D11—81no—
239C2×D11—81no—
240C2×D11—81no—
241C2×D11—81no—
242C4×C11—22no—
243C4×C11—42no—
244C4×C11—42no—
245C4×C11—81no—
246C4×C11—81no—
247C4×C11—82no—
248C4×C11#47814yes—
249C4×C11#53311yescharacteristic
250C4×C11#54411yescharacteristic
251C4×C11#55211yescharacteristic
252C4×C11#55311yescharacteristic
253Dic11—42no—
254Dic11—82no—
255C22×D4—111no—
256C23×C4—221no—
257C22×C8—111no—
258C22×C8—111no—
259C22×C8—112no—
260C4×D4—114no—
261C4×D4—222no—
262#117—444no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4C22⋊D1111yescharacteristic
271C2×C4⋊C4C22⋊D1111yescharacteristic
272C2×C4⋊C4C22×D1111yescharacteristic
273C2×C4⋊C4C22×D1111yescharacteristic
274C2×C4⋊C4C22×D1112yes—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—222no—
278C2×C42—21no—
279C2×C42—222no—
280C2×C42C22×D1112yes—
281C2×C42C22×D1111yescharacteristic
282#107—224no—
283#107—442no—
284#106—442no—
285C4⋊C8—224no—
286C4⋊C8—222no—
287#102—222no—
288#102—222no—
289#102—442no—
290C4×C8—222no—
291#95—21no—
292#95—22no—
293#95—22no—
294#95—22no—
295#95—222no—
296#95C22⋊D1112yes—
297C2×C11#244111yescharacteristic
298C2×C11C2×#47811yescharacteristic
299C2×C11#308311yescharacteristic
300C2×C11#334111yescharacteristic
301C2×C11#335311yescharacteristic
302C2×C11#339311yescharacteristic
303C2×C11#339911yescharacteristic
304D11—82no—
305C24—221no—
306C2×D4—112no—
307C2×D4—221no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—221no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—221no—
316C22×C4—224no—
317C22×C4—222no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4C2×C22⋊D1112yes—
321C22×C4C2×C22⋊D1112yes—
322C22×C4C2×C22⋊D1111yescharacteristic
323C22×C4C2×C22⋊D1111yescharacteristic
324C22×C4C23×D1111yescharacteristic
325C2×C8—112no—
326C2×C8—112no—
327C2×C8—221no—
328C2×C8—221no—
329C2×C8—221no—
330C2×C8—221no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—222no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—42no—
343C4⋊C4—81no—
344C4⋊C4—82no—
345C4⋊C4—112no—
346C4⋊C4—221no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—442no—
350C4⋊C4—881no—
351C22⋊C4—224no—
352C22⋊C4—444no—
353C22⋊C4—882no—
354C42—22no—
355C42—22no—
356C42—42no—
357C42—444no—
358C42Q8×D1112yes—
359C42#434312yes—
360C11#2608711yescharacteristic, complemented, Sylow
361C23—222no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23C22×C22⋊D1111yescharacteristic
369D4—222no—
370D4—222no—
371D4—441no—
372D4—441no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—222no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—448no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4#6699912yes—
398C2×C4#6699912yes—
399C2×C4#6700212yes—
400C2×C4#6700312yes—
401C2×C4C2×Q8×D1111yescharacteristic
402C2×C4C2×#434311yescharacteristic
403C2×C4#41×D1111yescharacteristic
404C2×C4#41×D1111yescharacteristic
405C2×C4#6704211yescharacteristic
406C2×C4#6704311yescharacteristic
407C8—222no—
408C8—222no—
409C8—442no—
410C22—442no—
411C22—442no—
412C22—442no—
413C22—881no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22C2×#6699911yescharacteristic
418C22C2×#6700211yescharacteristic
419C22C2×#6700311yescharacteristic
420C22#1062335511yescharacteristic
421C22#1062336511yescharacteristic
422C22#1062336611yescharacteristic
423C22#1062336911yescharacteristic
424C4—22no—
425C4—42no—
426C4—42no—
427C4—81no—
428C4—82no—
429C4—81no—
430C4—442no—
431C4—882no—
432C4#1062267914yes—
433C4#1062321911yescharacteristic
434C4#1062322011yescharacteristic
435C4#1062322511yescharacteristic
436C4#1062322611yescharacteristic
437C2—882no—
438C2#1307232511yescharacteristic
439C2C2×#1062267911yescharacteristic
440C2#1307846311yescharacteristic
441C2#1308103411yescharacteristic
442C2#1308119411yescharacteristic
443C2#1308160011yescharacteristic
444C2#1308165411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2571C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2571D11
hypocenterC11#26087
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2571

Complements

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

NH ≅ G/Ntype
4. #13069382C2semidirect
5. #13069379C2semidirect
6. #13069335C2semidirect
7. #13069205C2semidirect
8. #13068775C2semidirect
11. C11×#2571C2semidirect
139. #2571D11semidirect
360. C11#26087semidirect

Maximal subgroups

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

subgroupindex
#130715632
#130701402
#130700012
#130693822
#130693792
#130693352
#130692052
#130687752
#130686132
C4×#668732
C11×#25712
#2608711