Finite Group Databasebeta

← #14739257

Subgroups — #14739257

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078099C211yesmaximal, characteristic, complemented
2#13078065C211yesmaximal, characteristic
3#13077724C211yesmaximal, characteristic, complemented
4#13068057C212yesmaximal, complemented
5#13068050C212yesmaximal, complemented
6#13068007C212yesmaximal, complemented
7#13068002C212yesmaximal, complemented
8#13067391C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3226C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#67003—21no—
15C2×#66995—21no—
16C4×#4339C2211yescharacteristic
17C11×#500C2212yes—
18C11×#486C2212yes—
19C11×#480—22no—
20C11×#474—21no—
21C11×#474—21no—
22C11×#431C2211yescharacteristic
23#10622846—21no—
24#10622838—21no—
25#10622703—21no—
26#10622703C2212yes—
27#10622703C2211yescharacteristic
28#10622696—21no—
29#10622696C2212yes—
30#10622696C2211yescharacteristic
31#10622688C2211yescharacteristic
32#10622685C2211yescharacteristic
33#10622670—21no—
34#10622667—21no—
35#10622537C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622446—21no—
39D11×C4⋊C8—21no—
40(C22⋊D11)⋊C8—22no—
41C8×D44C2212yes—
42C8×Dic22C2212yes—
43#10622185C2212yes—
44#10622185C2212yes—
45#10622185C2212yes—
46#10622182C2212yes—
47#10622096C2212yes—
48#10622096C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11—21no—
51C2×#4339D411yescharacteristic
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2312yes—
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66#67003—44no—
67C2×#4326—22no—
68C2×#4326—21no—
69#66995—44no—
70C2×#4325—22no—
71C2×#4325—21no—
72C2×#4324—21no—
73C2×#4323—21no—
74C4×C22⋊D11—21no—
75C4×C22⋊D11—21no—
76#66979D411yescharacteristic
77C2×#4318—21no—
78C22×C11⋊C8—21no—
79C22×C11⋊C8—21no—
80C2×C8×D11—22no—
81C4×D44D411yescharacteristic
82C4×D44C2311yescharacteristic
83#66925—21no—
84C42×D11—21no—
85C4×Dic22D411yescharacteristic
86C4×Dic22C2311yescharacteristic
87C11×#107—22no—
88C11×#107—22no—
89C11×C4⋊C8D411yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×#102—22no—
92C11×#102—22no—
93C11×C22⋊C8D412yes—
94C4×C8×C11C2312yes—
95#66899—22no—
96#66899—22no—
97#66899—21no—
98#66899—21no—
99#66896—21no—
100#66896—21no—
101(C2×D11)⋊C8—22no—
102Dic11⋊C8—22no—
103C8×Dic11—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2311yescharacteristic
110C4⋊(C11⋊C8)C2312yes—
111#19416—111nomaximal, Sylow
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—41no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C2×C22⋊D11—21no—
129#4339—22no—
130#4339D814yes—
131C2×D44C2×D411yescharacteristic
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×Dic22C2×D411yescharacteristic
136C2×C8×C11C2×D412yes—
137C2×C8×C11C2×D412yes—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11#4111yescharacteristic
149C42×C11C2411yescharacteristic
150C22⋊Dic11—21no—
151#4326—44no—
152#4326—42no—
153#4325—44no—
154#4325—42no—
155#4324—42no—
156#4323—42no—
157(C2×D11)⋊C4—21no—
158(C2×D11)⋊C4—21no—
159C4⋊Dic11C2×D411yescharacteristic
160C4⋊Dic11C2×D411yescharacteristic
161Dic11⋊C4—21no—
162Dic11⋊C4—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172C2×C11⋊C8—81no—
173C8×D11—82no—
174#3226D1111yescharacteristic, complemented
175#3039—111no—
176#3035—111no—
177#2988—111no—
178#1682—112no—
179#1681—112no—
180#1674—112no—
181#1673—112no—
182#1571—111no—
183#1547—111no—
184C2×#332—111no—
185C23×C11—41no—
186C23×C11#12111yescharacteristic
187C22×D11—21no—
188Q8×C11—42no—
189Q8×C11—41no—
190Q8×C11—42no—
191Q8×C11—41no—
192Q8×C11—82no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—81no—
198D4×C11—82no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—82no—
205C2×C4×C11—82no—
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11C2×D812yes—
210C2×C4×C11#13512yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C22⋊D11—24no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218D44—21no—
219D44C2×D812yes—
220C4×D11—24no—
221C4×D11—41no—
222C4×D11—41no—
223C4×D11—81no—
224Dic22—21no—
225Dic22C2×D812yes—
226C8×C11—22no—
227C8×C11—22no—
228C11⋊C8—41no—
229C11⋊C8—41no—
230C11⋊C8—42no—
231C11⋊C8—42no—
232C2×#137—221no—
233C2×#135—221no—
234#532C2×D1111yescharacteristic
235C2×C4⋊Q8C2×D1111yescharacteristic
236C4×#41—111no—
237#500C2×D1112yes—
238#486C2×D1112yes—
239#480—22no—
240#474—21no—
241#474—21no—
242#464—221no—
243#463—221no—
244#462—111no—
245#462—112no—
246#462—221no—
247#461—111no—
248#461—112no—
249#461—221no—
250#460—111no—
251#459—111no—
252C8×Q8—112no—
253C8×D4—112no—
254C8×D4—222no—
255#431—221no—
256#431C2×D1111yescharacteristic
257#423—111no—
258C2×C4⋊C8—111no—
259C2×C4⋊C8—111no—
260C2×C4⋊C8—221no—
261#419—221no—
262#416—221no—
263#335—112no—
264#335—112no—
265#332—112no—
266#332—112no—
267#332—112no—
268#331—112no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11#46612yes—
275C22×C11C2×#12111yescharacteristic
276C2×D11—22no—
277C2×D11—41no—
278C2×D11—41no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—81no—
283C4×C11—82no—
284C4×C11#46612yes—
285C4×C11C22×D811yescharacteristic
286C4×C11C2×#13511yescharacteristic
287C4×C11#57711yescharacteristic
288C4×C11#57811yescharacteristic
289Dic11—22no—
290Dic11—41no—
291Dic11—41no—
292C2×#41—21no—
293C2×#41—111no—
294C22×Q8—21no—
295#137—444no—
296#135—444no—
297C2×Q16—221no—
298C2×Q16—222no—
299C2×SD16—221no—
300C2×SD16—221no—
301C2×SD16—222no—
302C2×D8—221no—
303C2×M16—221no—
304C22×C8—221no—
305C22×C8—221no—
306C22×C8—222no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8C22×D1112yes—
311C4⋊Q8C22×D1111yescharacteristic
312#127C22×D1111yescharacteristic
313#124—21no—
314#121—21no—
315#121—21no—
316C4×Q8—111no—
317C4×Q8—111no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—111no—
321C4×D4—111no—
322C4×D4—221no—
323C4×D4—221no—
324#117—111no—
325#117—221no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C42—221no—
329C2×C42C22×D1111yescharacteristic
330#107—22no—
331#107—22no—
332C4⋊C8—112no—
333C4⋊C8—112no—
334C4⋊C8—111no—
335C4⋊C8—111no—
336C4⋊C8—222no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339C4⋊C8—221no—
340C4⋊C8C22⋊D1111yescharacteristic
341C4⋊C8C22⋊D1111yescharacteristic
342#103—221no—
343#103—221no—
344#103—222no—
345#103—222no—
346#102—22no—
347#102—22no—
348#102—221no—
349#102—221no—
350C22⋊C8—222no—
351C22⋊C8C22⋊D1112yes—
352C4×C8—222no—
353C4×C8C22×D1112yes—
354C2×C11—22no—
355C2×C11—161no—
356C2×C11#304611yescharacteristic
357C2×C11C2×#46611yescharacteristic
358C2×C11#306911yescharacteristic
359D11—42no—
360#41—42no—
361#41—42no—
362#41—114no—
363#41—222no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—41no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8—111no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4—111no—
375C2×D4—221no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4D4×D1111yescharacteristic
382C22×C4#434111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384Q16—442no—
385Q16—444no—
386SD16—442no—
387SD16—442no—
388SD16—444no—
389D8—442no—
390M16—442no—
391C2×C8—221no—
392C2×C8—221no—
393C2×C8—222no—
394C2×C8—222no—
395C2×C8—442no—
396C2×C8—882no—
397C2×C8—881no—
398C2×C8C2×C22⋊D1112yes—
399C2×C8C2×C22⋊D1112yes—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—111no—
407C4⋊C4—111no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—221no—
413C22⋊C4—221no—
414C22⋊C4—221no—
415C42—221no—
416C42—221no—
417C42—221no—
418C42D4×D1111yescharacteristic
419C42#434111yescharacteristic
420C42C2×C22⋊D1111yescharacteristic
421C42C23×D1111yescharacteristic
422C11#1941611yescharacteristic, complemented, Sylow
423C23—41no—
424C23—221no—
425C23#6699111yescharacteristic
426Q8—42no—
427Q8—41no—
428Q8—42no—
429Q8—41no—
430Q8—82no—
431Q8—112no—
432Q8—221no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4—112no—
440D4—224no—
441D4—221no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—221no—
450C2×C4—224no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—881no—
456C2×C4D8×D1112yes—
457C2×C4#6696512yes—
458C2×C4#6699111yescharacteristic
459C2×C4#6699111yescharacteristic
460C2×C4#6699111yescharacteristic
461C2×C4C2×D4×D1111yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4C22×C22⋊D1111yescharacteristic
464C8—22no—
465C8—22no—
466C8—441no—
467C8—441no—
468C8—442no—
469C8—442no—
470C22—21no—
471C22—21no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—222no—
476C22—441no—
477C22—441no—
478C22#1062277012yes—
479C22C2×#6699111yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—81no—
484C4—82no—
485C4—222no—
486C4—441no—
487C4—441no—
488C4#1062277012yes—
489C4C2×D8×D1111yescharacteristic
490C4C2×#6696511yescharacteristic
491C4#1062336811yescharacteristic
492C4#1062336911yescharacteristic
493C2—22no—
494C2—161no—
495C2—442no—
496C2#1307816211yescharacteristic
497C2C2×#1062277011yescharacteristic
498C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3226C2
socleC22×C11C2×#121
prime radical#13078065C2
hypercenter#3226D11
hypocenterC11#19416
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
1. #13078099C2semidirect
3. #13077724C2semidirect
4. #13068057C2semidirect
5. #13068050C2semidirect
6. #13068007C2semidirect
7. #13068002C2semidirect
8. #13067391C2semidirect
9. #13067293C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3226C2semidirect
174. #3226D11semidirect
422. C11#19416semidirect

Maximal subgroups

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

subgroupindex
#130780992
#130780652
#130777242
#130680572
#130680502
#130680072
#130680022
#130673912
#130672932
C2×#106221852
C11×#32262
#1941611