Finite Group Databasebeta

← #14804155

Subgroups — #14804155

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
1C2×#10622700C211yesmaximal, characteristic, complemented
2#13078076C211yesmaximal, characteristic
3#13077360C211yesmaximal, characteristic, complemented
4#13070059C212yesmaximal, complemented
5#13069906C212yesmaximal, complemented
6#13069606C211yesmaximal, characteristic, complemented
7#13069391C211yesmaximal, characteristic, complemented
8#13069122C212yesmaximal, complemented
9#13068678C212yesmaximal, complemented
10C4×#66887C211yesmaximal, characteristic, complemented
11C11×#3141C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#67002C2212yes—
15C2×#67001C2212yes—
16C2×C4×D44C2211yescharacteristic
17C11×#489—22no—
18C11×#487—21no—
19C11×#486—21no—
20C11×#417C2212yes—
21C11×#417C2212yes—
22C4×C11×M16C2211yescharacteristic
23#10622847C2212yes—
24#10622845C2212yes—
25C2×#66887C2211yescharacteristic
26C2×#66887C2211yescharacteristic
27C2×#66886C2212yes—
28#10622700—21no—
29#10622700—22no—
30#10622700—21no—
31#10622696—21no—
32#10622685—21no—
33#10622670—22no—
34#10622625—21no—
35#10622624—22no—
36D4×C11⋊C8—21no—
37C2×#66873C2212yes—
38C2×#66871C2212yes—
39#10622537C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42#10622196C2212yes—
43#10622192C2211yescharacteristic
44#10622192C2211yescharacteristic
45#10622168C2212yes—
46#10622168C2212yes—
47C2×C11×#41C2312yes—
48C22×Q8×C11—21no—
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C2×C11×M16C2311yescharacteristic
52C2×C11×M16C2311yescharacteristic
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8D411yescharacteristic
58C11×#127D411yescharacteristic
59C11×#124D412yes—
60C11×#121—21no—
61C11×#121—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2312yes—
66C2×C42×C11C2311yescharacteristic
67#67002—24no—
68#67002—42no—
69#67001—24no—
70#67001—42no—
71C2×#4325—22no—
72C2×#4323—22no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×#4318—22no—
76C2×#4318C2312yes—
77C2×#4318C2311yescharacteristic
78C2×#4318C2311yescharacteristic
79C22×C11⋊C8—22no—
80C22×C11⋊C8C2312yes—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44—21no—
84C4×D44—21no—
85C11×#103—22no—
86C11×#103—22no—
87C11×#102—22no—
88C11×#102—22no—
89C11×#97—21no—
90C4×C8×C11—21no—
91#66899—22no—
92#66896—22no—
93C22⋊(C11⋊C8)—22no—
94C22⋊(C11⋊C8)—22no—
95#66887—22no—
96#66887—22no—
97#66886—42no—
98#66873—22no—
99#66873—22no—
100#66871—22no—
101#66871—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)D411yescharacteristic
105C4⋊(C11⋊C8)D412yes—
106C4⋊(C11⋊C8)D411yescharacteristic
107#66867—21no—
108C4×C11⋊C8—21no—
109#25358—111nomaximal, Sylow
110C23×D11—21no—
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—22no—
114C11×#41—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—82no—
118C2×Q8×C11C2×D412yes—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11C2×D412yes—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44#4112yes—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—82no—
138C11×M16—21no—
139C11×M16—21no—
140C11×M16—21no—
141C11×M16—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156#4325—44no—
157#4323—44no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162#4318—21no—
163#4318—22no—
164#4318—21no—
165#4318—22no—
166#4318—21no—
167#4318—44no—
168#4318#4112yes—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—44no—
175C2×C11⋊C8C2×D412yes—
176C2×C11⋊C8C2×D412yes—
177#3141D1111yescharacteristic, complemented
178C2×#474—111no—
179#3036—111no—
180#2935—111no—
181#2078—112no—
182#2051—112no—
183#1997—111no—
184#1950—111no—
185#1907—112no—
186#1816—112no—
187C4×#100—111no—
188C23×C11—22no—
189C23×C11C2×#4111yescharacteristic
190C22×D11—22no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—81no—
194C22×D11—81no—
195Q8×C11—22no—
196Q8×C11—22no—
197Q8×C11—82no—
198Q8×C11—82no—
199D4×C11—22no—
200D4×C11—22no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—81no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—82no—
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C2×C4×C112−1+411yescharacteristic
222C2×Dic11—41no—
223C2×Dic11—81no—
224D44—22no—
225D44—22no—
226D44—41no—
227D44—41no—
228C4×D11—82no—
229C4×D11—82no—
230C8×C11—41no—
231C8×C11—41no—
232C11⋊C8—22no—
233C11⋊C8—22no—
234C11⋊C8—22no—
235C11⋊C8—42no—
236C11⋊C8—41no—
237C2×AGL(1,ℤ/8)—112no—
238C2×#131—112no—
239#532C2×D1111yescharacteristic
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×C4×D4—111no—
242#489—22no—
243#487—21no—
244#486—21no—
245#474—221no—
246#474—222no—
247#474—221no—
248#463—222no—
249#461—221no—
250#459—221no—
251#436—221no—
252#435—222no—
253C8×D4—221no—
254C2×#108—112no—
255C2×#107—112no—
256#423—111no—
257C2×C4⋊C8—111no—
258#417—112no—
259#417C2×D1112yes—
260#417C2×D1112yes—
261C2×#102—112no—
262C2×#100—111no—
263C2×#100—111no—
264#408—112no—
265C4×M16—111no—
266C4×M16C2×D1111yescharacteristic
267#343—111no—
268#343—111no—
269#343—112no—
270#343—112no—
271#341—112no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11C2×#12111yescharacteristic
278C22×C11#52911yescharacteristic
279C22×C11#54211yescharacteristic
280C2×D11—42no—
281C2×D11—82no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—82no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—42no—
289C4×C11—82no—
290C4×C11#47212yes—
291C4×C11#54611yescharacteristic
292C4×C11#54611yescharacteristic
293C4×C11#54711yescharacteristic
294C4×C11#54811yescharacteristic
295Dic11—81no—
296C2×#41C22×D1112yes—
297C22×Q8—21no—
298C22×D4—111no—
299C23×C4—221no—
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—222no—
310C2×M16C22×D1111yescharacteristic
311C2×M16C22×D1111yescharacteristic
312C22×C8—112no—
313C22×C8—222no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8C22⋊D1111yescharacteristic
319#127C22⋊D1111yescharacteristic
320#124C22⋊D1112yes—
321#121—21no—
322#121—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—221no—
326C4×D4—221no—
327C4×D4—221no—
328C4×D4—221no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4C22×D1112yes—
332C2×C22⋊C4—221no—
333C2×C42C22×D1111yescharacteristic
334#108—442no—
335#107—222no—
336#107—222no—
337C4⋊C8—111no—
338C4⋊C8—112no—
339C4⋊C8—111no—
340C4⋊C8—221no—
341C4⋊C8—221no—
342#103—22no—
343#103—22no—
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—21no—
355#97—221no—
356C4×C8—21no—
357C4×C8—221no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11—82no—
361C2×C11#242711yescharacteristic
362C2×C11C2×#47211yescharacteristic
363C2×C11#306911yescharacteristic
364D11—82no—
365C24—221no—
366#41—22no—
367#41—22no—
368#41—22no—
369#41—22no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8—82no—
373C2×Q8C2×C22⋊D1112yes—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—112no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—221no—
381C2×D4—221no—
382C2×D4—221no—
383C2×D4C2×C22⋊D1112yes—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—221no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—882no—
390C22×C4#434111yescharacteristic
391C22×C4#434111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393SD16—444no—
394D8—444no—
395M16—21no—
396M16—21no—
397M16—21no—
398M16—21no—
399M16—112no—
400M16—221no—
401M16—221no—
402M16—222no—
403M16—222no—
404M16—221no—
405M16—444no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—112no—
409C2×C8—112no—
410C2×C8—221no—
411C2×C8—222no—
412C2×C8—222no—
413C2×C8—221no—
414C2×C8—222no—
415C2×C8—444no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C42D4×D1111yescharacteristic
429C42D4×D1111yescharacteristic
430C42C2×C22⋊D1111yescharacteristic
431C42C2×C22⋊D1111yescharacteristic
432C11#2535811yescharacteristic, complemented, Sylow
433C23—22no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—881no—
438C23—881no—
439C23C2×#434111yescharacteristic
440Q8—22no—
441Q8—22no—
442Q8—82no—
443Q8—82no—
444D4—22no—
445D4—22no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—81no—
450D4—222no—
451D4—222no—
452D4—441no—
453D4—441no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—82no—
461C2×C4—441no—
462C2×C4—882no—
463C2×C4—882no—
464C2×C4—881no—
465C2×C4#6699211yescharacteristic
466C2×C4#6699211yescharacteristic
467C2×C4#6699211yescharacteristic
468C2×C4#6699211yescharacteristic
469C2×C4C2×D4×D1111yescharacteristic
470C2×C4#41×D1111yescharacteristic
471C2×C4#41×D1111yescharacteristic
472C2×C4#6704211yescharacteristic
473C2×C4#6704311yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C8—41no—
476C8—41no—
477C8—222no—
478C8—222no—
479C8—222no—
480C8—442no—
481C8—441no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—442no—
488C22—882no—
489C22—882no—
490C22—881no—
491C22—881no—
492C22#1062321111yescharacteristic
493C22#1062321311yescharacteristic
494C22C2×#6699211yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—82no—
500C4—881no—
501C4#1062281212yes—
502C4#1062320711yescharacteristic
503C4#1062320811yescharacteristic
504C4#1062335511yescharacteristic
505C4#1062336011yescharacteristic
506C2—21no—
507C2—21no—
508C2—82no—
509C2—882no—
510C2#1307219611yescharacteristic
511C2C2×#1062281211yescharacteristic
512C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3141C2
socleC22×C11C2×#121
prime radical#13078076C2
hypercenter#3141D11
hypocenterC11#25358
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
3. #13077360C2semidirect
4. #13070059C2semidirect
5. #13069906C2semidirect
6. #13069606C2semidirect
7. #13069391C2semidirect
8. #13069122C2semidirect
9. #13068678C2semidirect
10. C4×#66887C2semidirect
11. C11×#3141C2semidirect
177. #3141D11semidirect
432. C11#25358semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
#130780762
#130773602
#130700592
#130699062
#130696062
#130693912
#130691222
#130686782
C4×#668872
C11×#31412
#2535811