Finite Group Databasebeta

← #14804159

Subgroups — #14804159

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079012C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13077359C211yesmaximal, characteristic, complemented
4#13070062C212yesmaximal, complemented
5#13069909C212yesmaximal, complemented
6#13069606C211yesmaximal, characteristic, complemented
7#13069392C211yesmaximal, characteristic, complemented
8#13069127C212yesmaximal, complemented
9#13068676C212yesmaximal, complemented
10C4×#66897C211yesmaximal, characteristic, complemented
11C2×C11×#476C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66985C2212yes—
15C2×#66954C2212yes—
16#10623008C2211yescharacteristic
17C11×#476—21no—
18C11×#476—22no—
19C11×#476—21no—
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102C2212yes—
23C2×#66897C2211yescharacteristic
24C2×#66897C2211yescharacteristic
25#10622723C2212yes—
26C2×#66883C2212yes—
27#10622706—21no—
28#10622702—22no—
29#10622701—21no—
30#10622632—21no—
31#10622629—22no—
32#10622628—21no—
33#10622579C2212yes—
34#10622579C2212yes—
35#10622579C2212yes—
36#10622537C2211yescharacteristic
37C4×#4318C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622451—21no—
40#10622449—22no—
41#10622447—21no—
42#10622190C2212yes—
43#10622168C2212yes—
44#10622168C2212yes—
45#10622168C2211yescharacteristic
46#10622168C2211yescharacteristic
47C22×Q8×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C2×#4339C2312yes—
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4324—22no—
66#66985—24no—
67#66985—42no—
68C2×#4323—22no—
69#66983—21no—
70#66983—21no—
71C2×#4318C2311yescharacteristic
72C2×#4318C2312yes—
73C2×#4318C2311yescharacteristic
74C2×#4318C2311yescharacteristic
75C2×#4318C2311yescharacteristic
76#66954—24no—
77#66954—42no—
78C2×#4313—22no—
79C2×C8×D11—22no—
80#66928D412yes—
81#66927D411yescharacteristic
82C4×D44—21no—
83C4×D44—21no—
84#66922D411yescharacteristic
85C11×#106—22no—
86C11×#106—22no—
87C11×C4⋊C8D411yescharacteristic
88C11×C4⋊C8D412yes—
89C11×C4⋊C8D411yescharacteristic
90C11×#102—22no—
91C11×#102—22no—
92#66897—22no—
93#66897—22no—
94(C2×D11)⋊C8—22no—
95(C2×D11)⋊C8—22no—
96#66883—42no—
97#66874—22no—
98#66874—22no—
99#66874—22no—
100#66873—22no—
101#66873—22no—
102#66873—22no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—21no—
109#25359—111nomaximal, Sylow
110C24×C11—21no—
111C2×Q8×C11—41no—
112C2×Q8×C11—41no—
113C2×Q8×C11—82no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11#4112yes—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—82no—
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—22no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132#4339—22no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44C2×D412yes—
136C2×C4×D11—22no—
137C2×Dic22C2×D412yes—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11C2×D412yes—
141C2×C8×C11C2×D412yes—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154#4324—44no—
155#4323—44no—
156(C2×D11)⋊C4—22no—
157(C2×D11)⋊C4—22no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160#4318—21no—
161#4318—21no—
162#4318—21no—
163#4318—22no—
164#4318—21no—
165#4318—21no—
166#4318—22no—
167#4318—21no—
168#4318—21no—
169#4318#4112yes—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175#4313—44no—
176C8×D11—44no—
177#3141—111no—
178C2×#476D1111yescharacteristic, complemented
179#3036—111no—
180#2935—111no—
181#2079—112no—
182#2051—112no—
183#1997—111no—
184#1950—111no—
185#1907—112no—
186#1815—112no—
187C4×#100—111no—
188C23×C11—22no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—81no—
192C23×C11—81no—
193C23×C11C2×#4111yescharacteristic
194C22×D11—22no—
195Q8×C11—82no—
196Q8×C11—82no—
197D4×C11—22no—
198D4×C11—22no—
199D4×C11—41no—
200D4×C11—41no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—82no—
206C2×C4×C11—82no—
207C2×C4×C11—81no—
208C2×C4×C11—82no—
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C22⋊D11—42no—
220C22⋊D11—42no—
221C2×Dic11—22no—
222D44—22no—
223D44—22no—
224D44—42no—
225D44—81no—
226C4×D11—42no—
227C4×D11—42no—
228Dic22—22no—
229Dic22—22no—
230C8×C11—22no—
231C8×C11—22no—
232C11⋊C8—22no—
233C11⋊C8—41no—
234C11⋊C8—42no—
235C11⋊C8—41no—
236C11⋊C8—41no—
237C2×AGL(1,ℤ/8)—112no—
238C2×#131—112no—
239#532—111no—
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×C4×D4C2×D1111yescharacteristic
242#489—222no—
243#487—221no—
244#486—221no—
245#476—21no—
246#476—22no—
247#476—21no—
248#463—222no—
249#461—221no—
250#459—221no—
251#436—221no—
252#435—222no—
253C8×D4—221no—
254C2×#108—112no—
255C2×#106C2×D1112yes—
256#423—111no—
257C2×C4⋊C8C2×D1111yescharacteristic
258#417—112no—
259#417—112no—
260#417—112no—
261C2×#102C2×D1112yes—
262C2×#100—111no—
263C2×#100—111no—
264#408—112no—
265C4×M16—111no—
266C4×M16—111no—
267#343—112no—
268#343—111no—
269#343—112no—
270#343—111no—
271#341—112no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—42no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11C2×#12111yescharacteristic
280C22×C11#52911yescharacteristic
281C22×C11#54211yescharacteristic
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—81no—
289C4×C11—82no—
290C4×C11#47112yes—
291C4×C11#54611yescharacteristic
292C4×C11#54611yescharacteristic
293C4×C11#54711yescharacteristic
294C4×C11#54811yescharacteristic
295Dic11—42no—
296C2×#41—112no—
297C22×Q8—21no—
298C22×D4C22×D1111yescharacteristic
299C23×C4—21no—
300AGL(1,ℤ/8)—224no—
301AGL(1,ℤ/8)—442no—
302C2×SD16—222no—
303C2×D8—222no—
304#131—224no—
305#131—442no—
306C2×M16—111no—
307C2×M16—112no—
308C2×M16—111no—
309C2×M16—111no—
310C2×M16—111no—
311C2×M16—222no—
312C22×C8—222no—
313C22×C8C22×D1112yes—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—111no—
319#127—111no—
320#124—112no—
321#121—221no—
322#121—221no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—221no—
328C4×D4—221no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C4⋊C4C22×D1112yes—
332C2×C22⋊C4—21no—
333C2×C42C22×D1111yescharacteristic
334#108—442no—
335#106—22no—
336#106—22no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339C4⋊C8C22⋊D1111yescharacteristic
340C4⋊C8C22⋊D1112yes—
341C4⋊C8C22⋊D1111yescharacteristic
342#103—222no—
343#103—222no—
344#103—222no—
345#102—22no—
346#102—22no—
347#102—222no—
348#102—222no—
349#102—222no—
350#100—222no—
351#100—222no—
352C22⋊C8—222no—
353C22⋊C8—222no—
354#97—221no—
355#97—221no—
356C4×C8—221no—
357C4×C8—221no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11—82no—
361C2×C11#242711yescharacteristic
362C2×C11C2×#47111yescharacteristic
363C2×C11#306811yescharacteristic
364D11—82no—
365C24—21no—
366#41—222no—
367#41—222no—
368#41—222no—
369#41—222no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8—82no—
373C2×Q8—112no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—112no—
380C2×D4—222no—
381C2×D4—221no—
382C2×D4—221no—
383C2×D4#434312yes—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—82no—
389C22×C4—222no—
390C22×C4#434111yescharacteristic
391C22×C4#434111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393SD16—444no—
394D8—444no—
395M16—112no—
396M16—221no—
397M16—221no—
398M16—221no—
399M16—222no—
400M16—221no—
401M16—221no—
402M16—221no—
403M16—221no—
404M16—222no—
405M16—444no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—221no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—222no—
412C2×C8—221no—
413C2×C8—444no—
414C2×C8C2×C22⋊D1112yes—
415C2×C8C2×C22⋊D1112yes—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—222no—
427C22⋊C4—222no—
428C42D4×D1111yescharacteristic
429C42D4×D1111yescharacteristic
430C42C2×C22⋊D1111yescharacteristic
431C42C2×C22⋊D1111yescharacteristic
432C11#2535911yescharacteristic, complemented, Sylow
433C23—22no—
434C23—41no—
435C23—41no—
436C23—81no—
437C23—81no—
438C23—222no—
439C23C2×#434111yescharacteristic
440Q8—82no—
441Q8—82no—
442Q8—222no—
443Q8—222no—
444D4—22no—
445D4—22no—
446D4—41no—
447D4—41no—
448D4—222no—
449D4—222no—
450D4—442no—
451D4—442no—
452D4—442no—
453D4—881no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—81no—
461C2×C4—82no—
462C2×C4—222no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4#6699111yescharacteristic
466C2×C4#6699111yescharacteristic
467C2×C4#6699111yescharacteristic
468C2×C4#6699111yescharacteristic
469C2×C4C2×D4×D1111yescharacteristic
470C2×C4C2×#434311yescharacteristic
471C2×C4#6704011yescharacteristic
472C2×C4#41×D1111yescharacteristic
473C2×C4#6704211yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C8—22no—
476C8—22no—
477C8—222no—
478C8—441no—
479C8—442no—
480C8—441no—
481C8—441no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—82no—
486C22—82no—
487C22—81no—
488C22—81no—
489C22—442no—
490C22—442no—
491C22—442no—
492C22#1062315511yescharacteristic
493C22#1062317411yescharacteristic
494C22C2×#6699111yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—81no—
499C4—82no—
500C4—442no—
501C4#1062279012yes—
502C4#1062316111yescharacteristic
503C4#1062316211yescharacteristic
504C4#1062334811yescharacteristic
505C4#1062336011yescharacteristic
506C2—21no—
507C2—21no—
508C2—82no—
509C2—882no—
510C2#1307218911yescharacteristic
511C2C2×#1062279011yescharacteristic
512C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC22×C11C2×#121
prime radical#13078080C2
hypercenterC2×#476D11
hypocenterC11#25359
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13079012C2semidirect
3. #13077359C2semidirect
4. #13070062C2semidirect
5. #13069909C2semidirect
6. #13069606C2semidirect
7. #13069392C2semidirect
8. #13069127C2semidirect
9. #13068676C2semidirect
10. C4×#66897C2semidirect
11. C2×C11×#476C2semidirect
178. C2×#476D11semidirect
432. C11#25359semidirect

Maximal subgroups

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

subgroupindex
#130790122
#130780802
#130773592
#130700622
#130699092
#130696062
#130693922
#130691272
#130686762
C4×#668972
C2×C11×#4762
#2535911