Finite Group Databasebeta

← #14739261

Subgroups — #14739261

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#13079739C211yesmaximal, characteristic, complemented
2#13078103C211yesmaximal, characteristic, complemented
3#13078071C211yesmaximal, characteristic
4#13068060C212yesmaximal, complemented
5#13068053C212yesmaximal, complemented
6#13068010C212yesmaximal, complemented
7#13068005C212yesmaximal, complemented
8#13067391C211yesmaximal, characteristic, complemented
9#13067291C211yesmaximal, characteristic, complemented
10C2×#10622124C211yesmaximal, characteristic, complemented
11C11×#2988C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67004—21no—
14C2×#67003—21no—
15#10623008C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C8×Q8×C11C2212yes—
18C8×D4×C11—22no—
19C8×D4×C11C2212yes—
20C11×#431—21no—
21C11×#431C2211yescharacteristic
22C2×C11×C4⋊C8—21no—
23C2×C11×C4⋊C8C2211yescharacteristic
24#10622644—21no—
25#10622644C2212yes—
26#10622644C2211yescharacteristic
27#10622641—21no—
28#10622640C2211yescharacteristic
29#10622632—21no—
30#10622632C2212yes—
31#10622632C2211yescharacteristic
32#10622629—21no—
33#10622628C2211yescharacteristic
34#10622617—21no—
35#10622615—21no—
36#10622537C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622459—21no—
39#10622459—21no—
40#10622349—22no—
41#10622307C2212yes—
42#10622295C2212yes—
43#10622124C2212yes—
44#10622124C2212yes—
45#10622124C2212yes—
46#10622123C2212yes—
47#10622096C2212yes—
48#10622096C2212yes—
49C2×C11×#41D411yescharacteristic
50C2×#4339—21no—
51C22×Dic22—21no—
52C22×C8×C11—21no—
53C22×C8×C11—22no—
54C4×Q8×C11D411yescharacteristic
55C4×Q8×C11C2311yescharacteristic
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D411yescharacteristic
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C11×#117D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#67004—44no—
65#67003—44no—
66C2×#4326—21no—
67C2×#4326—22no—
68C2×#4325—21no—
69C2×#4324—21no—
70C2×#4324—22no—
71C2×#4323—21no—
72#66983—21no—
73#66983—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×#4318—21no—
77C22×C11⋊C8—21no—
78#66928—21no—
79#66927C2311yescharacteristic
80C4×D44—21no—
81C4×D44—21no—
82#66922—21no—
83#66922—21no—
84#66922—21no—
85#66922C2312yes—
86#66922C2311yescharacteristic
87C11×C4⋊C8—22no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8D411yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×C4⋊C8C2312yes—
92C11×C22⋊C8—22no—
93C11×C22⋊C8D412yes—
94C4×C8×C11—22no—
95C4×C8×C11C2312yes—
96#66885—22no—
97#66885—22no—
98#66882—22no—
99#66882—22no—
100#66874—21no—
101#66874—21no—
102#66874—22no—
103#66874—22no—
104#66873—21no—
105#66873—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2311yescharacteristic
110C4⋊(C11⋊C8)C2312yes—
111#19416—111nomaximal, Sylow
112C11×#41—22no—
113C11×#41D814yes—
114C2×Q8×C11C2×D411yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11C2×D411yescharacteristic
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C2×C22⋊D11—41no—
124C22×Dic11—41no—
125#4339—42no—
126#4339—42no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×C4×D11—41no—
131C2×Dic22—22no—
132C2×Dic22—21no—
133C2×Dic22—41no—
134C2×Dic22—42no—
135C2×Dic22—42no—
136C2×C8×C11—22no—
137C2×C8×C11—81no—
138C2×C8×C11—82no—
139C2×C8×C11C2×D412yes—
140C2×C8×C11C2×D412yes—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4C2×D411yescharacteristic
144C11×C4⋊C4C2×D411yescharacteristic
145C11×C22⋊C4—21no—
146C11×C22⋊C4—21no—
147C11×C22⋊C4—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155#4326—42no—
156#4326—44no—
157#4325—42no—
158#4324—42no—
159#4324—44no—
160#4323—42no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163C4⋊Dic11—21no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—21no—
167C4⋊Dic11—41no—
168C4⋊Dic11—41no—
169#4318—42no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—42no—
174#3226—111no—
175#3039—111no—
176#3035—111no—
177#2988D1111yescharacteristic, complemented
178#1682—112no—
179#1681—112no—
180#1674—112no—
181#1673—112no—
182#1571—111no—
183#1547—111no—
184C2×#332—111no—
185C23×C11—21no—
186C23×C11#12111yescharacteristic
187C22×D11—41no—
188Q8×C11—21no—
189Q8×C11C2×D812yes—
190D4×C11—24no—
191D4×C11—21no—
192D4×C11C2×D812yes—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—81no—
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11C2×D812yes—
207C2×C4×C11#13512yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C22⋊D11—82no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214C2×Dic11—82no—
215D44—41no—
216D44—41no—
217D44—41no—
218D44—41no—
219D44—81no—
220C4×D11—82no—
221Dic22—42no—
222Dic22—41no—
223Dic22—42no—
224Dic22—41no—
225Dic22—82no—
226C8×C11—22no—
227C8×C11—22no—
228C8×C11—42no—
229C11⋊C8—41no—
230C11⋊C8—41no—
231C11⋊C8—42no—
232C2×#137—221no—
233C2×#135—221no—
234#532—111no—
235C2×C4⋊Q8—111no—
236C4×#41C2×D1111yescharacteristic
237#500—112no—
238#486—112no—
239#480—222no—
240#474—221no—
241#474—221no—
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×Q8C2×D1112yes—
253C8×D4—22no—
254C8×D4C2×D1112yes—
255#431—21no—
256#431C2×D1111yescharacteristic
257#423—111no—
258C2×C4⋊C8—21no—
259C2×C4⋊C8—111no—
260C2×C4⋊C8C2×D1111yescharacteristic
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—22no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11#46612yes—
275C22×C11C2×#12111yescharacteristic
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11#46612yes—
286C4×C11C22×D811yescharacteristic
287C4×C11C2×#13511yescharacteristic
288C4×C11#57711yescharacteristic
289C4×C11#57811yescharacteristic
290Dic11—82no—
291Dic11—81no—
292C2×#41—221no—
293C2×#41D4411yescharacteristic
294C22×Q8—221no—
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—21no—
305C22×C8—22no—
306C22×C8—221no—
307C4⋊Q8—112no—
308C4⋊Q8—111no—
309C4⋊Q8—221no—
310C4⋊Q8—221no—
311C4⋊Q8—221no—
312#127—111no—
313#124—221no—
314#121—221no—
315#121—221no—
316C4×Q8D4411yescharacteristic
317C4×Q8C22×D1111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—221no—
321C4×D4—221no—
322C4×D4D4411yescharacteristic
323C4×D4C22×D1111yescharacteristic
324#117—21no—
325#117D4411yescharacteristic
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C42—21no—
329C2×C42C22×D1111yescharacteristic
330#107—222no—
331#107—222no—
332C4⋊C8—22no—
333C4⋊C8—21no—
334C4⋊C8—112no—
335C4⋊C8—111no—
336C4⋊C8—111no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339C4⋊C8C22⋊D1111yescharacteristic
340C4⋊C8C22⋊D1111yescharacteristic
341C4⋊C8C22×D1112yes—
342#103—221no—
343#103—221no—
344#103—222no—
345#103—222no—
346#102—222no—
347#102—222no—
348#102—221no—
349#102—221no—
350C22⋊C8—22no—
351C22⋊C8C22⋊D1112yes—
352C4×C8—22no—
353C4×C8C22×D1112yes—
354C2×C11—22no—
355C2×C11—42no—
356C2×C11#304611yescharacteristic
357C2×C11C2×#46611yescharacteristic
358C2×C11#306911yescharacteristic
359D11—161no—
360#41—22no—
361#41—442no—
362#41—442no—
363#41D8814yes—
364C2×Q8—221no—
365C2×Q8—222no—
366C2×Q8—441no—
367C2×Q8—442no—
368C2×Q8—442no—
369C2×Q8C2×D4411yescharacteristic
370C2×D4—21no—
371C2×D4—221no—
372C2×D4—221no—
373C2×D4—221no—
374C2×D4—441no—
375C2×D4C2×D4411yescharacteristic
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4C2×D4411yescharacteristic
382C22×C4#433911yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384Q16—442no—
385Q16—444no—
386SD16—442no—
387SD16—442no—
388SD16—444no—
389D8—442no—
390M16—442no—
391C2×C8—22no—
392C2×C8—82no—
393C2×C8—81no—
394C2×C8—221no—
395C2×C8—221no—
396C2×C8—222no—
397C2×C8—442no—
398C2×C8C2×C22⋊D1112yes—
399C2×C8C2×C22⋊D1112yes—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—222no—
403C4⋊C4—221no—
404C4⋊C4—222no—
405C4⋊C4—221no—
406C4⋊C4—441no—
407C4⋊C4—441no—
408C4⋊C4C2×D4411yescharacteristic
409C4⋊C4C2×D4411yescharacteristic
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42C2×D4411yescharacteristic
419C42#433911yescharacteristic
420C42C2×C22⋊D1111yescharacteristic
421C42C23×D1111yescharacteristic
422C11#1941611yescharacteristic, complemented, Sylow
423C23—21no—
424C23—441no—
425C23#6698311yescharacteristic
426Q8—21no—
427Q8—442no—
428Q8—441no—
429Q8—442no—
430Q8—441no—
431Q8—882no—
432Q8C2×D8812yes—
433D4—24no—
434D4—21no—
435D4—441no—
436D4—441no—
437D4—441no—
438D4—441no—
439D4—881no—
440D4—882no—
441D4C2×D8812yes—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—81no—
452C2×C4—441no—
453C2×C4—442no—
454C2×C4—882no—
455C2×C4—882no—
456C2×C4C2×D8812yes—
457C2×C4#6695712yes—
458C2×C4#6698311yescharacteristic
459C2×C4#6698311yescharacteristic
460C2×C4#6698311yescharacteristic
461C2×C4C22×D4411yescharacteristic
462C2×C4C2×#433911yescharacteristic
463C2×C4C22×C22⋊D1111yescharacteristic
464C8—22no—
465C8—22no—
466C8—42no—
467C8—441no—
468C8—441no—
469C8—442no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22#1062272812yes—
479C22C2×#6698311yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—881no—
487C4—882no—
488C4#1062272812yes—
489C4C22×D8811yescharacteristic
490C4C2×#6695711yescharacteristic
491C4#1062336711yescharacteristic
492C4#1062336911yescharacteristic
493C2—22no—
494C2—42no—
495C2—1761no—
496C2#1307816611yescharacteristic
497C2C2×#1062272811yescharacteristic
498C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×#121
prime radical#13078071C2
hypercenter#2988D11
hypocenterC11#19416
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13079739C2semidirect
2. #13078103C2semidirect
4. #13068060C2semidirect
5. #13068053C2semidirect
6. #13068010C2semidirect
7. #13068005C2semidirect
8. #13067391C2semidirect
9. #13067291C2semidirect
10. C2×#10622124C2semidirect
11. C11×#2988C2semidirect
177. #2988D11semidirect
422. C11#19416semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130781032
#130780712
#130680602
#130680532
#130680102
#130680052
#130673912
#130672912
C2×#106221242
C11×#29882
#1941611