Finite Group Databasebeta

← #14795241

Subgroups — #14795241

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078431C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3#13077282C211yesmaximal, characteristic, complemented
4#13070064C212yesmaximal, complemented
5#13069905C212yesmaximal
6#13069605C211yesmaximal, characteristic, complemented
7#13069393C212yesmaximal, complemented
8#13069391C211yesmaximal, characteristic, complemented
9#13069281C212yesmaximal, complemented
10#13068608C211yesmaximal, characteristic, complemented
11C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
12C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
13C4×C11×#41C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#442—21no—
17C11×#440—21no—
18C4×C11×SD16—21no—
19C4×C11×D8—21no—
20C11×#428C2211yescharacteristic
21C11×#418C2211yescharacteristic
22C11×#417C2211yescharacteristic
23C4×C11×M16C2211yescharacteristic
24#10622847C2212yes—
25#10622845C2212yes—
26C2×#66897C2212yes—
27C2×#66896C2212yes—
28C2×#66886C2212yes—
29#10622634—21no—
30#10622633—21no—
31#10622621—21no—
32#10622621—21no—
33#10622621—21no—
34#10622621—22no—
35#10622620—21no—
36#10622613—22no—
37#10622610C2212yes—
38#10622608C2212yes—
39C2×#66872C2212yes—
40#10622539—21no—
41#10622538—21no—
42#10622537C2211yescharacteristic
43#10622537C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622196C2212yes—
46#10622192C2212yes—
47#10622192C2212yes—
48#10622168C2212yes—
49C2×C11×#41C2311yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C22×Dic22—21no—
53C11×AGL(1,ℤ/8)—22no—
54C11×AGL(1,ℤ/8)—22no—
55C2×C11×SD16—21no—
56C2×C11×D8—21no—
57C2×C11×M16C2311yescharacteristic
58C2×C11×M16C2311yescharacteristic
59C4×Q8×C11D411yescharacteristic
60C4×Q8×C11D411yescharacteristic
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11D411yescharacteristic
68C4×D4×C11D411yescharacteristic
69C11×#117—21no—
70C11×#117C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2312yes—
77C2×#4318C2312yes—
78C2×#4318C2312yes—
79C22×C11⋊C8C2312yes—
80#66922—21no—
81#66922—21no—
82#66922—21no—
83#66922—21no—
84C11×#107—21no—
85C11×#106—21no—
86C11×#103—21no—
87C11×#102—21no—
88C11×#102—21no—
89C11×#102—21no—
90C11×#97—21no—
91C4×C8×C11—21no—
92#66899—22no—
93#66897—24no—
94#66896—22no—
95#66896—22no—
96#66896—22no—
97C22⋊(C11⋊C8)—22no—
98C22⋊(C11⋊C8)—22no—
99#66886—24no—
100#66872—22no—
101#66872—22no—
102#66872—22no—
103#66871—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)D411yescharacteristic
109C4⋊(C11⋊C8)D411yescharacteristic
110C4⋊(C11⋊C8)D412yes—
111#66867—22no—
112C4×C11⋊C8—22no—
113#24721—111nomaximal, Sylow
114C24×C11—21no—
115C11×#41—21no—
116C11×#41—21no—
117C11×#41—21no—
118C11×#41—21no—
119C2×Q8×C11C2×D411yescharacteristic
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C2×D411yescharacteristic
127C2×D4×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11—82no—
135C22×C4×C11#4111yescharacteristic
136C22×C4×C11#4111yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—22no—
139C2×Dic22—41no—
140C2×Dic22—41no—
141C2×Dic22—82no—
142C11×SD16—24no—
143C11×D8—24no—
144C11×M16—21no—
145C11×M16—21no—
146C11×M16—21no—
147C11×M16#4112yes—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4C2×D411yescharacteristic
155C11×C4⋊C4C2×D411yescharacteristic
156C11×C22⋊C4—21no—
157C11×C22⋊C4—21no—
158C11×C22⋊C4—21no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—41no—
171C4⋊Dic11—41no—
172#4318—22no—
173#4318—22no—
174#4318—22no—
175#4318—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8C2×D412yes—
181C2×C11⋊C8C2×D412yes—
182#3079—111no—
183C2×#476—111no—
184C4×AGL(1,ℤ/8)D1111yescharacteristic
185#2925—111no—
186#2079—112no—
187#2051—112no—
188#1997—111no—
189#1951—112no—
190#1950—111no—
191#1931—112no—
192#1800—111no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—81no—
198C23×C11—81no—
199C23×C11C2×#4111yescharacteristic
200Q8×C11—21no—
201Q8×C11—21no—
202D4×C11—21no—
203D4×C11—22no—
204D4×C11—21no—
205D4×C11—22no—
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—41no—
210C2×C4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—81no—
220C2×C4×C11—82no—
221C2×C4×C11—82no—
222C2×C4×C11—81no—
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C112−1+411yescharacteristic
232C2×C4×C112−1+411yescharacteristic
233C2×Dic11—42no—
234C2×Dic11—82no—
235Dic22—82no—
236Dic22—82no—
237C8×C11—22no—
238C8×C11—41no—
239C11⋊C8—22no—
240C11⋊C8—22no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
244C2×C4⋊Q8—111no—
245C4×#41C2×D1111yescharacteristic
246C2×C4×D4C2×D1111yescharacteristic
247#477—221no—
248#476—221no—
249#476—221no—
250#476—222no—
251#476—221no—
252#475—221no—
253#474—221no—
254#442—21no—
255#440—21no—
256C4×SD16—21no—
257C4×D8—21no—
258#433—222no—
259#432—221no—
260#431—221no—
261C2×#108—112no—
262#428—112no—
263#428C2×D1111yescharacteristic
264C2×#106—112no—
265#423—111no—
266#423—111no—
267C2×C4⋊C8—111no—
268#418C2×D1111yescharacteristic
269#417—112no—
270#417C2×D1111yescharacteristic
271C2×#102—112no—
272C2×#100—112no—
273#408—112no—
274#405—112no—
275C4×M16C2×D1111yescharacteristic
276#343—112no—
277#343—112no—
278#343—112no—
279#341—112no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—41no—
283C22×C11—42no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11C2×#12111yescharacteristic
291C22×C11#55211yescharacteristic
292C22×C11#55611yescharacteristic
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—81no—
300C4×C11#47112yes—
301C4×C11#52511yescharacteristic
302C4×C11#53611yescharacteristic
303C4×C11#54711yescharacteristic
304C4×C11#54811yescharacteristic
305Dic11—82no—
306C2×#41C22×D1111yescharacteristic
307C22×Q8—221no—
308C22×D4C22×D1111yescharacteristic
309C23×C4—21no—
310AGL(1,ℤ/8)—22no—
311AGL(1,ℤ/8)—22no—
312C2×SD16—21no—
313C2×D8—21no—
314C2×M16—112no—
315C2×M16—112no—
316C2×M16C22×D1111yescharacteristic
317C2×M16C22×D1111yescharacteristic
318C22×C8—112no—
319C4⋊Q8—221no—
320C4⋊Q8—221no—
321C4⋊Q8—221no—
322C4⋊Q8—221no—
323C4×Q8C22⋊D1111yescharacteristic
324C4×Q8C22⋊D1111yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4C22⋊D1111yescharacteristic
332C4×D4C22⋊D1111yescharacteristic
333#117—21no—
334#117C22×D1111yescharacteristic
335C2×C4⋊C4—112no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4C22×D1111yescharacteristic
338C2×C22⋊C4—21no—
339C2×C42—21no—
340C2×C42C22×D1111yescharacteristic
341#108—224no—
342#107—21no—
343#107—222no—
344#106—21no—
345#106—222no—
346#106—222no—
347#106—222no—
348C4⋊C8—111no—
349C4⋊C8—111no—
350C4⋊C8—112no—
351C4⋊C8—221no—
352C4⋊C8—221no—
353C4⋊C8—221no—
354C4⋊C8—221no—
355#103—21no—
356#103—222no—
357#102—21no—
358#102—21no—
359#102—21no—
360#102—222no—
361#102—222no—
362#102—222no—
363#100—224no—
364C22⋊C8—222no—
365C22⋊C8—222no—
366#97—21no—
367#97—222no—
368C4×C8—21no—
369C4×C8—222no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—81no—
373C2×C11—82no—
374C2×C11#241511yescharacteristic
375C2×C11C2×#47111yescharacteristic
376C2×C11#306811yescharacteristic
377C24—21no—
378#41—21no—
379#41—21no—
380#41—21no—
381#41—21no—
382C2×Q8—441no—
383C2×Q8—441no—
384C2×Q8—882no—
385C2×Q8C2×C22⋊D1111yescharacteristic
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4#433912yes—
393C2×D4C2×C22⋊D1111yescharacteristic
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—82no—
401C22×C4—222no—
402C22×C4#434111yescharacteristic
403C22×C4#434111yescharacteristic
404C22×C4C23×D1111yescharacteristic
405SD16—24no—
406D8—24no—
407M16—21no—
408M16—21no—
409M16—21no—
410M16—222no—
411M16—222no—
412M16—222no—
413M16—222no—
414M16#433912yes—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—112no—
418C2×C8—112no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—222no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—222no—
428C4⋊C4—222no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4C2×C22⋊D1111yescharacteristic
432C4⋊C4C2×C22⋊D1111yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C42—21no—
439C42—21no—
440C42—21no—
441C42D4×D1111yescharacteristic
442C42D4×D1111yescharacteristic
443C42C2×C22⋊D1111yescharacteristic
444C42C2×C22⋊D1111yescharacteristic
445C11#2472111yescharacteristic, complemented, Sylow
446C23—21no—
447C23—22no—
448C23—41no—
449C23—41no—
450C23—81no—
451C23—81no—
452C23C2×#434111yescharacteristic
453Q8—21no—
454Q8—21no—
455Q8—882no—
456Q8—882no—
457D4—21no—
458D4—22no—
459D4—22no—
460D4—21no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—41no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—81no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—81no—
478C2×C4—442no—
479C2×C4—882no—
480C2×C4#6699211yescharacteristic
481C2×C4#6699211yescharacteristic
482C2×C4#6699211yescharacteristic
483C2×C4#6699211yescharacteristic
484C2×C4C2×#433911yescharacteristic
485C2×C4C2×#433911yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C2×C4#6704311yescharacteristic
488C2×C4#6704311yescharacteristic
489C2×C4C22×C22⋊D1111yescharacteristic
490C8—22no—
491C8—41no—
492C8—222no—
493C8—222no—
494C8—442no—
495C8—442no—
496C22—21no—
497C22—21no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—42no—
502C22—82no—
503C22—82no—
504C22—81no—
505C22—81no—
506C22#1062307211yescharacteristic
507C22#1062307311yescharacteristic
508C22C2×#6699211yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—81no—
516C4—882no—
517C4#1062281312yes—
518C4#1062308211yescharacteristic
519C4#1062308311yescharacteristic
520C4#1062332211yescharacteristic
521C4#1062335611yescharacteristic
522C2—21no—
523C2—21no—
524C2—81no—
525C2—82no—
526C2#1307204511yescharacteristic
527C2C2×#1062281311yescharacteristic
528C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C2×#121
prime radicalC2×C11×AGL(1,ℤ/8)C22
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11#24721
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #13078431C2semidirect
2. C2×#10622621C2semidirect
3. #13077282C2semidirect
4. #13070064C2semidirect
6. #13069605C2semidirect
7. #13069393C2semidirect
8. #13069391C2semidirect
9. #13069281C2semidirect
10. #13068608C2semidirect
445. C11#24721semidirect

Maximal subgroups

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

subgroupindex
#130784312
C2×#106226212
#130772822
#130700642
#130699052
#130696052
#130693932
#130693912
#130692812
#130686082
C4×C11×AGL(1,ℤ/8)2
#2472111