Finite Group Databasebeta

← #14811859

Subgroups — #14811859

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073645C211yesmaximal, characteristic, complemented
2#13071567C211yesmaximal, characteristic
3#13070005C212yesmaximal
4#13069751C212yesmaximal
5#13069566C212yesmaximal, complemented
6#13069372C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13069185C212yesmaximal, complemented
9#13068613C211yesmaximal, characteristic
10C4×#66885C211yesmaximal, characteristic
11C11×#1834C211yesmaximal, characteristic, complemented
12C2×#66945—21no—
13C2×#66941—21no—
14C2×#66941C2212yes—
15C2×C4×D44C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C11×#384C2211yescharacteristic
18C11×#384C2211yescharacteristic
19C2×#66885C2211yescharacteristic
20C2×#66885C2211yescharacteristic
21C2×Dic11⋊C8C2212yes—
22#10622603—22no—
23#10622601C2212yes—
24#10622600—21no—
25#10622592—22no—
26C4⋊C4×Dic11C2212yes—
27#10622586—21no—
28#10622586C2212yes—
29C2×#66873C2212yes—
30C2×#66871C2212yes—
31C4×C4⋊Dic11C2211yescharacteristic
32C4×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34C11×#340C2212yes—
35C11×#340C2212yes—
36#10622189C2211yescharacteristic
37#10622189C2211yescharacteristic
38#10622188C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C22×Dic22—22no—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2312yes—
52C2×C42×C11C2311yescharacteristic
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11C2312yes—
66C22×C11⋊C8C2312yes—
67#66945—44no—
68#66941—24no—
69#66941—42no—
70#66941—44no—
71C4×D44—22no—
72C4×D44Q814yescomplemented
73C4×C8×C11—22no—
74C11⋊#95—21no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95D412yes—
78#66885—22no—
79#66885—22no—
80Dic11⋊C8—42no—
81#66873—42no—
82#66871—24no—
83C4⋊(C11⋊C8)—22no—
84#26020—111nomaximal, Sylow
85C23×D11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11C2×D412yes—
95C22×Dic11C2×D412yes—
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—
105C2×Dic22—44no—
106C2×Dic22—44no—
107C2×Dic22—82no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—81no—
121C11×C4⋊C4—81no—
122C42×C11C2×Q812yes—
123C42×C11#4112yes—
124(C2×D11)⋊C4—24no—
125(C2×D11)⋊C4—44no—
126(C2×D11)⋊C4—82no—
127C4⋊Dic11—22no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11D814yes—
132C4⋊Dic11C2×Q812yes—
133C4⋊Dic11#4112yes—
134C4⋊Dic11#4112yes—
135Dic11⋊C4—44no—
136Dic11⋊C4—44no—
137C4×Dic11—22no—
138C4×Dic11—22no—
139C4×Dic11—44no—
140C4×Dic11—42no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144#2551—111no—
145#2354—111no—
146#2067—112no—
147#2023—112no—
148#1988—112no—
149#1947—111no—
150#1939—111no—
151#1918—112no—
152#1834D1111yescharacteristic, complemented
153#1802—111no—
154C4×#102—111no—
155C23×C11C22×D411yescharacteristic
156C22×D11—22no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11C22⋊Q812yes—
172C2×C4×C11C22⋊Q812yes—
173C2×C4×C11C2×D812yes—
174C2×C4×C11#13712yes—
175C2×C4×C11C22×Q811yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C11H(5,𝔽2)11yescharacteristic
180C2×C4×C112−1+411yescharacteristic
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11C2×D814yes—
196D44—22no—
197D44—22no—
198D44—41no—
199D44—41no—
200C4×D11—48no—
201Dic22—88no—
202C8×C11—41no—
203C8×C11—41no—
204C11⋊C8—42no—
205C2×C4⋊Q8—112no—
206C2×C4⋊Q8—221no—
207C2×C4×D4—111no—
208C2×#117—221no—
209C2×#107—112no—
210C2×C4⋊C8—111no—
211C2×C4⋊C8—112no—
212C2×#102—111no—
213C2×#102—111no—
214C2×#102—112no—
215C2×C4×C8C2×D1111yescharacteristic
216#395—222no—
217#390—112no—
218#389—112no—
219#389—221no—
220#388—222no—
221#384C2×D1111yescharacteristic
222#384C2×D1111yescharacteristic
223#380—221no—
224C4×C4⋊C4—111no—
225C4×C4⋊C4—112no—
226C4×C4⋊C4—111no—
227#340—111no—
228#340—111no—
229#340—112no—
230#340—112no—
231#340C2×D1112yes—
232#340C2×D1112yes—
233#336—112no—
234C22×C11C2×C22⋊Q811yescharacteristic
235C22×C11#54611yescharacteristic
236C22×C11#54811yescharacteristic
237C22×C11C22×D811yescharacteristic
238C22×C11C2×#13711yescharacteristic
239C22×C11#57711yescharacteristic
240C22×C11#57711yescharacteristic
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—81no—
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C4×C11—22no—
249C4×C11—82no—
250C4×C11—82no—
251C4×C11#47414yes—
252C4×C11#53311yescharacteristic
253C4×C11#54411yescharacteristic
254C4×C11#55511yescharacteristic
255C4×C11#55611yescharacteristic
256Dic11—24no—
257Dic11—42no—
258Dic11—42no—
259Dic11—42no—
260Dic11—42no—
261C22×Q8—222no—
262C22×D4—111no—
263C23×C4—221no—
264C22×C8—112no—
265C22×C8C22×D1111yescharacteristic
266C22×C8C22×D1111yescharacteristic
267C4⋊Q8—224no—
268C4⋊Q8—442no—
269C4⋊Q8—444no—
270C4×D4—114no—
271C4×D4—222no—
272#117—444no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—111no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4C22×D1112yes—
285C2×C4⋊C4C22×D1112yes—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—222no—
288C2×C22⋊C4—222no—
289C2×C42—112no—
290C2×C42—222no—
291C2×C42—221no—
292C2×C42C22×D1111yescharacteristic
293#107—224no—
294C4⋊C8—222no—
295C4⋊C8—442no—
296#102—222no—
297#102—222no—
298#102—442no—
299C4×C8—22no—
300#95—112no—
301#95—222no—
302#95—222no—
303#95—221no—
304C2×C11#243911yescharacteristic
305C2×C11C2×#47411yescharacteristic
306C2×C11#308411yescharacteristic
307C2×C11#329411yescharacteristic
308C2×C11#332911yescharacteristic
309C2×C11#335811yescharacteristic
310C2×C11#336911yescharacteristic
311D11—82no—
312C24—221no—
313C2×Q8—444no—
314C2×Q8—444no—
315C2×Q8—882no—
316C2×D4—112no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—221no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—112no—
325C22×C4—112no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—224no—
330C22×C4—442no—
331C22×C4—442no—
332C22×C4D4×D1111yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4C23×D1111yescharacteristic
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—222no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—81no—
351C4⋊C4—81no—
352C4⋊C4—114no—
353C4⋊C4—112no—
354C4⋊C4—112no—
355C4⋊C4—112no—
356C4⋊C4—222no—
357C4⋊C4—221no—
358C4⋊C4—221no—
359C4⋊C4—221no—
360C4⋊C4—444no—
361C4⋊C4—444no—
362C22⋊C4—224no—
363C22⋊C4—444no—
364C22⋊C4—882no—
365C42—222no—
366C42—222no—
367C42—444no—
368C42—442no—
369C42#433912yes—
370C42Q8×D1112yes—
371C11#2602011yescharacteristic, complemented, Sylow
372C23—222no—
373C23—441no—
374C23—441no—
375C23—441no—
376C23—441no—
377C23—441no—
378C23—441no—
379C23C2×D4×D1111yescharacteristic
380Q8—888no—
381D4—222no—
382D4—222no—
383D4—441no—
384D4—441no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—114no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—448no—
409C2×C4#6694912yes—
410C2×C4#6694912yes—
411C2×C4D8×D1112yes—
412C2×C4#6697112yes—
413C2×C4C2×#433911yescharacteristic
414C2×C4C2×Q8×D1111yescharacteristic
415C2×C4#41×D1111yescharacteristic
416C2×C4#41×D1111yescharacteristic
417C2×C4#6704211yescharacteristic
418C2×C4#6704311yescharacteristic
419C8—41no—
420C8—41no—
421C8—442no—
422C22—442no—
423C22—442no—
424C22—442no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22C2×#6694911yescharacteristic
430C22#1062320711yescharacteristic
431C22#1062320811yescharacteristic
432C22C2×D8×D1111yescharacteristic
433C22#1062329311yescharacteristic
434C22#1062329311yescharacteristic
435C22C2×#6697111yescharacteristic
436C4—22no—
437C4—82no—
438C4—82no—
439C4—224no—
440C4—442no—
441C4—442no—
442C4—442no—
443C4—442no—
444C4#1062250314yes—
445C4#1062306311yescharacteristic
446C4#1062306411yescharacteristic
447C4#1062321911yescharacteristic
448C4#1062322011yescharacteristic
449C2—882no—
450C2#1307231011yescharacteristic
451C2C2×#1062250311yescharacteristic
452C2#1307848311yescharacteristic
453C2#1308042811yescharacteristic
454C2#1308090911yescharacteristic
455C2#1308124811yescharacteristic
456C2#1308136111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1834C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1834D11
hypocenterC11#26020
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
1. #13073645C2semidirect
5. #13069566C2semidirect
6. #13069372C2semidirect
7. #13069334C2semidirect
8. #13069185C2semidirect
11. C11×#1834C2semidirect
72. C4×D44Q8semidirect
152. #1834D11semidirect
371. C11#26020semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130715672
#130700052
#130697512
#130695662
#130693722
#130693342
#130691852
#130686132
C4×#668852
C11×#18342
#2602011