Finite Group Databasebeta

← #14812730

Subgroups — #14812730

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071563C211yesmaximal, characteristic
2#13070145C212yesmaximal
3#13070001C212yesmaximal
4#13069374C211yesmaximal, characteristic, complemented
5#13069372C212yesmaximal, complemented
6#13069335C211yesmaximal, characteristic, complemented
7#13069184C212yesmaximal, complemented
8#13068775C211yesmaximal, characteristic, complemented
9#13068613C211yesmaximal, characteristic
10C4×#66873C211yesmaximal, characteristic
11C11×#2552C211yesmaximal, characteristic, complemented
12C2×C11×#125—21no—
13C2×#66945—21no—
14C2×C4×D44C2211yescharacteristic
15C11×#398—22no—
16C11×#389—21no—
17C11×#389C2212yes—
18C11×#384C2212yes—
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22#10622600—21no—
23C2×#66873C2211yescharacteristic
24C2×#66873C2211yescharacteristic
25C2×#66873C2212yes—
26C2×#66871C2212yes—
27C2×#66871C2212yes—
28C2×#66871C2212yes—
29#10622552C2212yes—
30#10622548C2211yescharacteristic
31C4×C4⋊Dic11C2212yes—
32C2×C4⋊(C11⋊C8)C2212yes—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622283—22no—
36#10622167C2211yescharacteristic
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2211yescharacteristic
40#10622162C2212yes—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C11×#125—44no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4×Dic11—22no—
65C22×C11⋊C8C2312yes—
66C22×C11⋊C8C2311yescharacteristic
67C22×C11⋊C8C2311yescharacteristic
68#66945—44no—
69C4×D44—22no—
70C4×D44Q814yes—
71C11×#95—21no—
72C11×#95—22no—
73C11×#95D412yes—
74C11⋊#95—22no—
75#66873—22no—
76#66873—22no—
77#66873—42no—
78#66871—24no—
79#66871—42no—
80#66871—42no—
81C4⋊(C11⋊C8)—22no—
82C4⋊(C11⋊C8)—24no—
83C4×C11⋊C8—22no—
84#26086—111nomaximal, Sylow
85C23×D11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—22no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44C2×Q812yes—
102C2×C4×D11—24no—
103C2×C4×D11—42no—
104C2×C4×D11—42no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—44no—
113C11×C4⋊C4—44no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—81no—
116C11×C4⋊C4—82no—
117C11×C4⋊C4D814yes—
118C42×C11—22no—
119C42×C11—22no—
120C42×C11—42no—
121C42×C11C2×Q812yes—
122C42×C11#4112yes—
123(C2×D11)⋊C4—24no—
124(C2×D11)⋊C4—44no—
125(C2×D11)⋊C4—82no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—42no—
130C4⋊Dic11—81no—
131C4⋊Dic11C2×Q812yes—
132C4×Dic11—44no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8#4112yes—
141C2×C11⋊C8#4112yes—
142#2552D1111yescharacteristic, complemented
143#2354—111no—
144#2093—112no—
145#2067—112no—
146#1947—112no—
147#1947—111no—
148#1939—111no—
149#1918—112no—
150#1845—111no—
151#1802—111no—
152C4×#102—111no—
153C23×C11C22×D411yescharacteristic
154C22×D11—22no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C2×C4×C11—22no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11C22⋊Q812yes—
178C2×C4×C11C22⋊Q812yes—
179C2×C4×C11C2×D814yes—
180C2×C4×C11C2×D812yes—
181C2×C4×C11#13712yes—
182C2×C4×C11C22×Q811yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11H(5,𝔽2)11yescharacteristic
187C2×C4×C112−1+411yescharacteristic
188C2×Dic11—22no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194D44—22no—
195D44—22no—
196D44—41no—
197D44—41no—
198C4×D11—48no—
199C11⋊C8—22no—
200C11⋊C8—22no—
201C11⋊C8—42no—
202C2×#125—21no—
203C2×C4×D4—111no—
204C2×#117—221no—
205C2×#107—112no—
206C2×#107—112no—
207C2×#107—112no—
208C2×C4⋊C8—111no—
209C2×C4⋊C8—112no—
210C2×#102—111no—
211C2×#102—111no—
212C2×#102—112no—
213C2×C4×C8—111no—
214#398—22no—
215#390—112no—
216#389—21no—
217#389C2×D1112yes—
218#388—222no—
219#384—111no—
220#384C2×D1111yescharacteristic
221#384C2×D1112yes—
222#380—221no—
223C4×C4⋊C4—112no—
224C4×C4⋊C4C2×D1111yescharacteristic
225C4×C4⋊C4C2×D1111yescharacteristic
226#340—112no—
227#340—112no—
228#340—111no—
229#340—111no—
230#336—112no—
231C22×C11C2×C22⋊Q811yescharacteristic
232C22×C11#54711yescharacteristic
233C22×C11#55011yescharacteristic
234C22×C11C22×D811yescharacteristic
235C22×C11C2×#13711yescharacteristic
236C22×C11#57611yescharacteristic
237C22×C11#57811yescharacteristic
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—42no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C4×C11—24no—
246C4×C11—22no—
247C4×C11—42no—
248C4×C11—81no—
249C4×C11—81no—
250C4×C11—82no—
251C4×C11#47414yes—
252C4×C11#53311yescharacteristic
253C4×C11#54411yescharacteristic
254C4×C11#55211yescharacteristic
255C4×C11#55311yescharacteristic
256Dic11—42no—
257Dic11—82no—
258C22×D4—111no—
259C23×C4—221no—
260C22×C8—111no—
261C22×C8—111no—
262C22×C8—112no—
263#125—44no—
264C4×D4—114no—
265C4×D4—222no—
266#117—444no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4C22⋊D1111yescharacteristic
277C2×C4⋊C4C22⋊D1111yescharacteristic
278C2×C4⋊C4C22×D1111yescharacteristic
279C2×C4⋊C4C22×D1111yescharacteristic
280C2×C4⋊C4C22×D1112yes—
281C2×C22⋊C4—221no—
282C2×C22⋊C4—222no—
283C2×C22⋊C4—222no—
284C2×C42—21no—
285C2×C42—222no—
286C2×C42C22×D1112yes—
287C2×C42C22×D1111yescharacteristic
288#107—224no—
289#107—442no—
290#107—442no—
291C4⋊C8—224no—
292C4⋊C8—222no—
293#102—222no—
294#102—222no—
295#102—442no—
296C4×C8—222no—
297#95—21no—
298#95—22no—
299#95—222no—
300#95C22⋊D1112yes—
301C2×C11#244111yescharacteristic
302C2×C11C2×#47411yescharacteristic
303C2×C11#308311yescharacteristic
304C2×C11#333411yescharacteristic
305C2×C11#335711yescharacteristic
306C2×C11#339111yescharacteristic
307C2×C11#339811yescharacteristic
308D11—82no—
309C24—221no—
310C2×D4—112no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—221no—
314C2×D4—221no—
315C2×D4—221no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—221no—
320C22×C4—224no—
321C22×C4—222no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4C2×C22⋊D1112yes—
325C22×C4C2×C22⋊D1112yes—
326C22×C4C2×C22⋊D1111yescharacteristic
327C22×C4C2×C22⋊D1111yescharacteristic
328C22×C4C23×D1111yescharacteristic
329C2×C8—112no—
330C2×C8—112no—
331C2×C8—221no—
332C2×C8—221no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—222no—
338C4⋊C4—22no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—44no—
346C4⋊C4—44no—
347C4⋊C4—42no—
348C4⋊C4—81no—
349C4⋊C4—82no—
350C4⋊C4—112no—
351C4⋊C4—221no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—442no—
355C4⋊C4—881no—
356C4⋊C4#432314yes—
357C22⋊C4—224no—
358C22⋊C4—444no—
359C22⋊C4—882no—
360C42—22no—
361C42—22no—
362C42—42no—
363C42—444no—
364C42Q8×D1112yes—
365C42#434312yes—
366C11#2608611yescharacteristic, complemented, Sylow
367C23—222no—
368C23—441no—
369C23—441no—
370C23—441no—
371C23—441no—
372C23—441no—
373C23—441no—
374C23C22×C22⋊D1111yescharacteristic
375D4—222no—
376D4—222no—
377D4—441no—
378D4—441no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—222no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—448no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4C2×#432314yes—
403C2×C4C2×#432312yes—
404C2×C4#6699512yes—
405C2×C4#6699912yes—
406C2×C4#6699912yes—
407C2×C4C2×Q8×D1111yescharacteristic
408C2×C4C2×#434311yescharacteristic
409C2×C4#41×D1111yescharacteristic
410C2×C4#41×D1111yescharacteristic
411C2×C4#6704211yescharacteristic
412C2×C4#6704311yescharacteristic
413C8—222no—
414C8—222no—
415C8—442no—
416C22—442no—
417C22—442no—
418C22—442no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22—881no—
423C22C22×#432311yescharacteristic
424C22C2×#6699511yescharacteristic
425C22C2×#6699911yescharacteristic
426C22#1062335511yescharacteristic
427C22#1062336511yescharacteristic
428C22#1062336611yescharacteristic
429C22#1062336911yescharacteristic
430C4—24no—
431C4—22no—
432C4—42no—
433C4—81no—
434C4—81no—
435C4—82no—
436C4—442no—
437C4—882no—
438C4#1062270014yes—
439C4#1062321911yescharacteristic
440C4#1062322011yescharacteristic
441C4#1062322511yescharacteristic
442C4#1062322611yescharacteristic
443C2—882no—
444C2#1307232511yescharacteristic
445C2C2×#1062270011yescharacteristic
446C2#1307846311yescharacteristic
447C2#1308095911yescharacteristic
448C2#1308124211yescharacteristic
449C2#1308158811yescharacteristic
450C2#1308164311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2552C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2552D11
hypocenterC11#26086
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2552

Complements

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

NH ≅ G/Ntype
4. #13069374C2semidirect
5. #13069372C2semidirect
6. #13069335C2semidirect
7. #13069184C2semidirect
8. #13068775C2semidirect
11. C11×#2552C2semidirect
142. #2552D11semidirect
366. C11#26086semidirect

Maximal subgroups

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

subgroupindex
#130715632
#130701452
#130700012
#130693742
#130693722
#130693352
#130691842
#130687752
#130686132
C4×#668732
C11×#25522
#2608611