Finite Group Databasebeta

← #14737319

Subgroups — #14737319

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079741C211yesmaximal, characteristic, complemented
2#13079009C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13068189C212yesmaximal, complemented
5#13068147C212yesmaximal, complemented
6#13068065C212yesmaximal, complemented
7#13068023C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9C2×#10622119C211yesmaximal, characteristic, complemented
10#13067265C211yesmaximal, characteristic, complemented
11C11×#3245C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#67001—21no—
15C2×#66922C2211yescharacteristic
16C11×#474—21no—
17C11×#474C2212yes—
18C11×#466—22no—
19C11×#459—21no—
20C11×#459C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22#10622847—21no—
23#10622845—21no—
24#10622845—21no—
25#10622694C2212yes—
26#10622692—21no—
27#10622683—21no—
28#10622683C2212yes—
29#10622668—22no—
30#10622647—22no—
31#10622625C2212yes—
32#10622624—22no—
33D4×C11⋊C8C2212yes—
34#10622621C2212yes—
35#10622621C2212yes—
36#10622538C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622185C2211yescharacteristic
40#10622185C2211yescharacteristic
41#10622182C2211yescharacteristic
42#10622182C2211yescharacteristic
43#10622119C2212yes—
44#10622119C2212yes—
45#10622118C2212yes—
46#10622117C2212yes—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C22×Dic22—21no—
50C2×C11×D8—22no—
51C22×C8×C11—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#127D411yescharacteristic
55C11×#127C2311yescharacteristic
56C11×#124—21no—
57C11×#124—21no—
58C11×#121—21no—
59C11×#121—21no—
60C11×#121—21no—
61C11×#121D412yes—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11C2312yes—
66C2×C42×C11C2311yescharacteristic
67#67001—44no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×#4318—22no—
71C2×#4318D411yescharacteristic
72C2×#4318D411yescharacteristic
73C22×C11⋊C8—21no—
74C22×C11⋊C8—22no—
75#66922—21no—
76#66922—21no—
77#66922—21no—
78#66922C2312yes—
79C11×#107—22no—
80C11×C4⋊C8—21no—
81C11×C4⋊C8C2312yes—
82C11×#102—22no—
83C11×#102—22no—
84#66899—22no—
85#66899—22no—
86#66896—22no—
87#66896—22no—
88#66896—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—21no—
91C22⋊(C11⋊C8)—22no—
92C22⋊(C11⋊C8)—22no—
93#66872—22no—
94#66872—22no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867D412yes—
101C4×C11⋊C8—21no—
102C4×C11⋊C8C2312yes—
103#19236—111nomaximal, Sylow
104C11×#41—42no—
105C11×#41—42no—
106C11×#41—42no—
107C11×#41—42no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C2×D4×C11C2×D412yes—
118C22×C4×C11—22no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×Dic11—41no—
124C2×Dic22—22no—
125C2×Dic22—41no—
126C2×Dic22—82no—
127C11×D8—82no—
128C2×C8×C11—22no—
129C2×C8×C11—81no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4C2×D412yes—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11#4111yescharacteristic
141C42×C11C2411yescharacteristic
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146#4318—22no—
147#4318—22no—
148#4318—44no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—44no—
154C2×C11⋊C8—42no—
155C2×C11⋊C8C2×D412yes—
156C2×C11⋊C8C2×D412yes—
157#3245D1111yescharacteristic
158#3227—111no—
159#3141—111no—
160#2935—111no—
161#1703—112no—
162#1697—112no—
163#1683—112no—
164#1677—112no—
165#1565—111no—
166C2×#333—111no—
167#1540—111no—
168C23×C11—22no—
169C23×C11—41no—
170C23×C11#12111yescharacteristic
171Q8×C11—42no—
172Q8×C11—41no—
173Q8×C11—41no—
174D4×C11—22no—
175D4×C11—22no—
176D4×C11—44no—
177D4×C11—41no—
178D4×C11—41no—
179D4×C11—41no—
180D4×C11—41no—
181D4×C11—42no—
182D4×C11—81no—
183D4×C11—81no—
184D4×C11—82no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—82no—
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#13512yes—
197C2×C4×C11AGL(1,ℤ/8)12yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×Dic11—42no—
202C2×Dic11—82no—
203Dic22—82no—
204Dic22—82no—
205C8×C11—42no—
206C11⋊C8—22no—
207C11⋊C8—22no—
208C11⋊C8—41no—
209C11⋊C8—41no—
210C11⋊C8—41no—
211C11⋊C8—41no—
212C2×#131—221no—
213#532C2×D1111yescharacteristic
214#532C2×D1111yescharacteristic
215C2×C4⋊Q8—111no—
216#498—221no—
217#489—222no—
218#487—112no—
219#486—112no—
220#486—221no—
221#481—222no—
222#476—112no—
223#476—112no—
224#474—21no—
225#474C2×D1112yes—
226#466—22no—
227#459—21no—
228#459C2×D1112yes—
229#436—112no—
230#435—222no—
231C8×D4—112no—
232#431—111no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8C2×D1111yescharacteristic
235#417—221no—
236#417—221no—
237#408—221no—
238C4×M16—111no—
239#335—112no—
240#334—112no—
241#333—112no—
242#333—112no—
243#332—111no—
244#332—111no—
245#331—111no—
246#331—111no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11#46312yes—
256C22×C11C2×#12111yescharacteristic
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11—81no—
262C4×C11#46312yes—
263C4×C11C2×#13511yescharacteristic
264C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C4×C11#57711yescharacteristic
266C4×C11#57811yescharacteristic
267Dic11—82no—
268C2×#41—21no—
269C2×#41—21no—
270C22×Q8—221no—
271C2×D8—22no—
272#131—444no—
273C2×M16—111no—
274C2×M16—111no—
275C2×M16—222no—
276C22×C8—21no—
277C22×C8—222no—
278C22×C8—221no—
279C4⋊Q8—112no—
280C4⋊Q8—221no—
281C4⋊Q8—221no—
282C4⋊Q8—221no—
283C4⋊Q8C22⋊D1111yescharacteristic
284C4⋊Q8C22×D1111yescharacteristic
285#127C22⋊D1111yescharacteristic
286#127C22×D1111yescharacteristic
287#124—21no—
288#124—21no—
289#121—21no—
290#121—21no—
291#121—21no—
292#121C22⋊D1112yes—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4C22×D1112yes—
297C2×C4⋊C4—221no—
298C2×C4⋊C4—221no—
299C2×C42C22×D1111yescharacteristic
300#107—22no—
301#106—222no—
302#106—222no—
303C4⋊C8—21no—
304C4⋊C8—111no—
305C4⋊C8—111no—
306C4⋊C8—111no—
307C4⋊C8—111no—
308C4⋊C8—221no—
309C4⋊C8C22×D1112yes—
310#103—222no—
311#103—222no—
312#102—22no—
313#102—22no—
314#102—222no—
315#102—222no—
316#102—222no—
317#102—222no—
318C22⋊C8—222no—
319C22⋊C8—222no—
320C22⋊C8—221no—
321#97—112no—
322C4×C8—112no—
323C4×C8—221no—
324C2×C11—22no—
325C2×C11—82no—
326C2×C11—161no—
327C2×C11C2×#46311yescharacteristic
328C2×C11#306311yescharacteristic
329C2×C11#306811yescharacteristic
330#41—42no—
331#41—42no—
332#41—42no—
333#41—42no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—222no—
337C2×Q8—441no—
338C2×Q8—882no—
339C2×D4—22no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—41no—
346C2×D4C2×C22⋊D1112yes—
347C22×C4—22no—
348C22×C4—41no—
349C22×C4—441no—
350C22×C4D4×D1111yescharacteristic
351C22×C4#434111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353D8—82no—
354M16—222no—
355M16—222no—
356M16—444no—
357C2×C8—22no—
358C2×C8—81no—
359C2×C8—112no—
360C2×C8—112no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8—444no—
366C2×C8—442no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4C2×C22⋊D1112yes—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C42D4×D1111yescharacteristic
380C42#434111yescharacteristic
381C42C2×C22⋊D1111yescharacteristic
382C42C23×D1111yescharacteristic
383C11#1923611yescharacteristic, complemented, Sylow
384C23—22no—
385C23—41no—
386C23#6699211yescharacteristic
387Q8—42no—
388Q8—41no—
389Q8—41no—
390Q8—882no—
391Q8—882no—
392D4—22no—
393D4—22no—
394D4—44no—
395D4—42no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—41no—
400D4—81no—
401D4—81no—
402D4—82no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—82no—
411C2×C4—442no—
412C2×C4—882no—
413C2×C4#6696412yes—
414C2×C4#6696512yes—
415C2×C4#6699211yescharacteristic
416C2×C4#6699211yescharacteristic
417C2×C4#6699211yescharacteristic
418C2×C4C2×D4×D1111yescharacteristic
419C2×C4C2×#434111yescharacteristic
420C2×C4C22×C22⋊D1111yescharacteristic
421C8—42no—
422C8—222no—
423C8—222no—
424C8—441no—
425C8—441no—
426C8—441no—
427C8—441no—
428C22—21no—
429C22—21no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22#1062276612yes—
437C22C2×#6699211yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—81no—
443C4—882no—
444C4#1062276612yes—
445C4C2×#6696411yescharacteristic
446C4C2×#6696511yescharacteristic
447C4#1062336711yescharacteristic
448C4#1062336911yescharacteristic
449C2—22no—
450C2—82no—
451C2—161no—
452C2C2×#1062276611yescharacteristic
453C2#1307830911yescharacteristic
454C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3245C2
socleC22×C11C2×#121
hypercenter#3245D11
hypocenterC11#19236
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
2. #13079009C2semidirect
3. #13077360C2semidirect
4. #13068189C2semidirect
5. #13068147C2semidirect
6. #13068065C2semidirect
7. #13068023C2semidirect
8. #13067366C2semidirect
9. C2×#10622119C2semidirect
10. #13067265C2semidirect
383. C11#19236semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130790092
#130773602
#130681892
#130681472
#130680652
#130680232
#130673662
C2×#106221192
#130672652
C11×#32452
#1923611