Finite Group Databasebeta

← #14812739

Subgroups — #14812739

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#13073855C211yesmaximal, characteristic, complemented
2#13070137C212yesmaximal
3#13070004C212yesmaximal
4#13069384C212yesmaximal, complemented
5#13069377C211yesmaximal, characteristic, complemented
6#13069335C211yesmaximal, characteristic, complemented
7#13069208C212yesmaximal, complemented
8#13068775C211yesmaximal, characteristic, complemented
9#13068616C211yesmaximal, characteristic
10C4×#66896C211yesmaximal, characteristic
11C11×#2354C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×C11×#117—21no—
14C11×#390C2212yes—
15C11×#388—22no—
16C11×#384C2211yescharacteristic
17C11×#380—21no—
18C4×C11×C4⋊C4C2212yes—
19C4×C11×C4⋊C4C2211yescharacteristic
20C2×#66896C2211yescharacteristic
21C2×#66896C2211yescharacteristic
22C2×#66896C2212yes—
23#10622590—21no—
24#10622586—21no—
25C2×#66872C2212yes—
26C2×#66871C2212yes—
27C2×#66871C2212yes—
28#10622549C2212yes—
29#10622548C2211yescharacteristic
30C4×C4⋊Dic11C2211yescharacteristic
31#10622541C2212yes—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622273—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2211yescharacteristic
39#10622167C2211yescharacteristic
40#10622162C2212yes—
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C4×D4×C11—22no—
44C4×D4×C11Q814yes—
45C11×#117—44no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11—22no—
56C2×C42×C11C2312yes—
57C2×C42×C11C2311yescharacteristic
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—22no—
64C2×C4×Dic11—21no—
65C22×C11⋊C8C2312yes—
66C22×C11⋊C8C2311yescharacteristic
67C22×C11⋊C8C2311yescharacteristic
68C11×#95—22no—
69C11×#95D412yes—
70#66896—22no—
71#66896—22no—
72#66896—42no—
73C11⋊#95—21no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
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
84C24×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11C2×Q812yes—
91C22×C4×C11—21no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—81no—
111C11×C4⋊C4C2×Q812yes—
112C11×C22⋊C4—24no—
113C11×C22⋊C4—44no—
114C11×C22⋊C4—82no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—44no—
118C42×C11C2×Q812yes—
119C42×C11#4112yes—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—42no—
127C4⋊Dic11—81no—
128Dic11⋊C4—82no—
129C4×Dic11—42no—
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#2571—111no—
140#2354D1111yescharacteristic
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×C11—22no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11C22×D411yescharacteristic
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—41no—
161D4×C11—41no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—48no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11C22⋊Q812yes—
178C2×C4×C11C22⋊Q812yes—
179C2×C4×C11#13512yes—
180C2×C4×C11AGL(1,ℤ/8)12yes—
181C2×C4×C11C22×Q811yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11H(5,𝔽2)11yescharacteristic
186C2×C4×C112−1+411yescharacteristic
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—42no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—42no—
193C2×Dic11—41no—
194C2×Dic11—42no—
195C2×Dic11—41no—
196C11⋊C8—22no—
197C11⋊C8—22no—
198C11⋊C8—42no—
199C2×C4×D4C2×D1111yescharacteristic
200C2×#117—21no—
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—222no—
211#390C2×D1112yes—
212#389—112no—
213#389—221no—
214#388—22no—
215#384—111no—
216#384C2×D1111yescharacteristic
217#382—112no—
218#382—221no—
219#380—21no—
220C4×C4⋊C4—111no—
221C4×C4⋊C4C2×D1112yes—
222C4×C4⋊C4C2×D1111yescharacteristic
223#340—112no—
224#340—112no—
225#340—111no—
226#340—111no—
227#336—112no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11C2×C22⋊Q811yescharacteristic
236C22×C11#54711yescharacteristic
237C22×C11#55011yescharacteristic
238C22×C11C2×#13511yescharacteristic
239C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
240C22×C11#57611yescharacteristic
241C22×C11#57811yescharacteristic
242C4×C11—22no—
243C4×C11—42no—
244C4×C11—42no—
245C4×C11—42no—
246C4×C11—82no—
247C4×C11#47814yes—
248C4×C11#53311yescharacteristic
249C4×C11#54411yescharacteristic
250C4×C11#55211yescharacteristic
251C4×C11#55311yescharacteristic
252Dic11—81no—
253Dic11—81no—
254Dic11—82no—
255C22×D4C22×D1111yescharacteristic
256C23×C4—21no—
257C22×C8—111no—
258C22×C8—111no—
259C22×C8—112no—
260C4×D4—22no—
261C4×D4Dic2214yes—
262#117—44no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—222no—
271C2×C4⋊C4C22⋊D1111yescharacteristic
272C2×C4⋊C4C22⋊D1111yescharacteristic
273C2×C4⋊C4C22×D1112yes—
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C42—22no—
279C2×C42—221no—
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—22no—
292#95—221no—
293#95—222no—
294#95—222no—
295#95—222no—
296#95C22⋊D1112yes—
297C2×C11—82no—
298C2×C11#244111yescharacteristic
299C2×C11C2×#47811yescharacteristic
300C2×C11#308311yescharacteristic
301C2×C11#334111yescharacteristic
302C2×C11#335311yescharacteristic
303C2×C11#339311yescharacteristic
304C2×C11#339911yescharacteristic
305C24—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4C2×Dic2212yes—
312C22×C4—21no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—222no—
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—22no—
338C4⋊C4—22no—
339C4⋊C4—42no—
340C4⋊C4—81no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—442no—
348C4⋊C4—882no—
349C4⋊C4—881no—
350C4⋊C4C2×Dic2212yes—
351C22⋊C4—24no—
352C22⋊C4—44no—
353C22⋊C4—82no—
354C42—22no—
355C42—22no—
356C42—44no—
357C42—442no—
358C42C2×Dic2212yes—
359C42#433912yes—
360C11#2608711yescharacteristic, complemented, Sylow
361C23—22no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23C22×C22⋊D1111yescharacteristic
369D4—22no—
370D4—22no—
371D4—41no—
372D4—41no—
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—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—48no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—442no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4#6697712yes—
398C2×C4#6697712yes—
399C2×C4#6698512yes—
400C2×C4#6700312yes—
401C2×C4C22×Dic2211yescharacteristic
402C2×C4C2×#433911yescharacteristic
403C2×C4#41×D1111yescharacteristic
404C2×C4#41×D1111yescharacteristic
405C2×C4#6704211yescharacteristic
406C2×C4#6704311yescharacteristic
407C8—222no—
408C8—222no—
409C8—442no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22C2×#6697711yescharacteristic
418C22C2×#6698511yescharacteristic
419C22C2×#6700311yescharacteristic
420C22#1062335511yescharacteristic
421C22#1062336511yescharacteristic
422C22#1062336611yescharacteristic
423C22#1062336911yescharacteristic
424C4—22no—
425C4—42no—
426C4—42no—
427C4—42no—
428C4—82no—
429C4—881no—
430C4—882no—
431C4—881no—
432C4#1062262214yes—
433C4#1062304811yescharacteristic
434C4#1062305011yescharacteristic
435C4#1062306011yescharacteristic
436C4#1062306111yescharacteristic
437C2—82no—
438C2#1307232311yescharacteristic
439C2C2×#1062262211yescharacteristic
440C2#1307846711yescharacteristic
441C2#1308103411yescharacteristic
442C2#1308120011yescharacteristic
443C2#1308160011yescharacteristic
444C2#1308165811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2354D11
hypocenterC11#26087
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. #13073855C2semidirect
4. #13069384C2semidirect
5. #13069377C2semidirect
6. #13069335C2semidirect
7. #13069208C2semidirect
8. #13068775C2semidirect
360. C11#26087semidirect

Maximal subgroups

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

subgroupindex
#130738552
#130701372
#130700042
#130693842
#130693772
#130693352
#130692082
#130687752
#130686162
C4×#668962
C11×#23542
#2608711