Finite Group Databasebeta

← C22×#11718239 #16796822

Subgroups — C22×#11718239 #16796822

Order 3328.

2190 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6122C211yesmaximal, characteristic
2C23×#6122C211yesmaximal, characteristic
3C2×#11718239C2112yesmaximal, direct product factor
4C22×#88131C211yesmaximal, characteristic
5C24×Dic13C2211yescharacteristic
6C22×#6122—23no—
7C22×#6122—21no—
8C22×#6122—21no—
9C22×#6122—23no—
10C22×#6122—23no—
11C22×#6122—21no—
12C22×#6122—23no—
13C22×#6122C412yescomplemented
14C22×#6122C416yescomplemented
15C22×#6122C416yescomplemented
16C22×#6122C2216yes—
17C22×#6122C2216yes—
18C23×#1057—21no—
19C23×#1057C412yescomplemented
20C22×C13×C22⋊C4C411yescharacteristic
21C22×C22⋊Dic13C411yescharacteristic
22C22×#6101—21no—
23C22×C4×Dic13—21no—
24C2×#88131—23no—
25C2×#88131—23no—
26C2×#88131C416yes—
27C2×#88131C2216yes—
28#11718239C22116yesdirect product factor
29C25×C13C2×C411yescharacteristic
30C23×C4×C13—21no—
31C23×Dic13—21no—
32C23×Dic13C2×C413yes—
33C23×Dic13C2×C411yescharacteristic
34C23×Dic13C2×C411yescharacteristic
35C23×Dic13C2×C413yes—
36C23×Dic13C2×C413yes—
37C23×Dic13D411yescharacteristic
38C23×Dic13D413yes—
39C23×Dic13D413yes—
40C23×Dic13D413yes—
41C23×Dic13D411yescharacteristic
42C23×Dic13D411yescharacteristic
43C23×Dic13Q811yescharacteristic
44C23×Dic13Q813yes—
45C23×Dic13C2313yes—
46C2×#6122—26no—
47C2×#6122—26no—
48C2×#6122—212no—
49C2×#6122—26no—
50C2×#6122—26no—
51C2×#6122—212no—
52C2×#6122—26no—
53C2×#6122—26no—
54C2×#6122—26no—
55C2×#6122—26no—
56C2×#6122—26no—
57C2×#6122—26no—
58C2×#6122—26no—
59C2×#6122C2×C4112yescomplemented
60C2×#6122C2×C4112yescomplemented
61C2×#6122C2×C4112yescomplemented
62C2×#6122C2314yes—
63C2×#6122C2314yes—
64C22×#1057—26no—
65C22×#1057—22no—
66C22×#1057—26no—
67C22×#1057—22no—
68C22×#1057—26no—
69C22×#1057C2×C4112yescomplemented
70C2×C13×C22⋊C4—23no—
71C2×C13×C22⋊C4C2×C416yes—
72C2×C22⋊Dic13—23no—
73C2×C22⋊Dic13C2×C416yes—
74C2×#6101—26no—
75C2×#6101—26no—
76C2×C4×Dic13—26no—
77C2×C4×Dic13—26no—
78#88131—212no—
79#88131—26no—
80#88131—26no—
81#88131C2×C4112yes—
82#88131C2314yes—
83C22×#344—131nomaximal, Sylow
84C24×C13—44no—
85C24×C13C4211yescharacteristic
86C24×C13C4213yes—
87C24×C13C22⋊C411yescharacteristic
88C24×C13C22⋊C413yes—
89C24×C13C4⋊C411yescharacteristic
90C24×C13C4⋊C413yes—
91C24×C13C22×C413yes—
92C22×C4×C13—26no—
93C22×C4×C13—44no—
94C22×Dic13—26no—
95C22×Dic13—44no—
96C22×Dic13C4213yes—
97C22×Dic13C4213yes—
98C22×Dic13C4216yes—
99C22×Dic13C22⋊C416yes—
100C22×Dic13C22⋊C413yes—
101C22×Dic13C22⋊C413yes—
102C22×Dic13C22⋊C413yes—
103C22×Dic13C22⋊C413yes—
104C22×Dic13C22⋊C411yescharacteristic
105C22×Dic13C22⋊C411yescharacteristic
106C22×Dic13C22⋊C413yes—
107C22×Dic13C22⋊C413yes—
108C22×Dic13C22⋊C413yes—
109C22×Dic13C22⋊C413yes—
110C22×Dic13C22⋊C416yes—
111C22×Dic13C22⋊C416yes—
112C22×Dic13C4⋊C413yes—
113C22×Dic13C4⋊C413yes—
114C22×Dic13C4⋊C416yes—
115C22×Dic13C4⋊C413yes—
116C22×Dic13C4⋊C413yes—
117C22×Dic13C4⋊C413yes—
118C22×Dic13C4⋊C413yes—
119C22×Dic13C4⋊C413yes—
120C22×Dic13C4⋊C413yes—
121C22×Dic13C4⋊C416yes—
122C22×Dic13C4⋊C416yes—
123C22×Dic13C4⋊C411yescharacteristic
124C22×Dic13C4⋊C411yescharacteristic
125C22×Dic13C22×C413yes—
126C22×Dic13C22×C413yes—
127C22×Dic13C22×C413yes—
128C22×Dic13C22×C413yes—
129C22×Dic13C22×C413yes—
130C22×Dic13C2×D413yes—
131C22×Dic13C2×D413yes—
132C22×Dic13C2×D413yes—
133C22×Dic13C2×D413yes—
134C22×Dic13C2×D413yes—
135C22×Dic13C2×D413yes—
136C22×Dic13C2×Q813yes—
137C22×Dic13C2×Q813yes—
138C22×Dic13C2411yescharacteristic
139#6122—212no—
140#6122—212no—
141#6122—212no—
142#6122—212no—
143#6122—24no—
144#6122—24no—
145#6122—24no—
146#6122C22×C418yescomplemented
147C2×#1057—212no—
148C2×#1057—212no—
149C2×#1057—212no—
150C2×#1057—212no—
151C2×#1057—24no—
152C2×#1057C22×C418yescomplemented
153C13×C22⋊C4—26no—
154C13×C22⋊C4C22×C414yes—
155C22⋊Dic13—26no—
156C22⋊Dic13C22×C414yes—
157#6101—212no—
158#6101—24no—
159C4×Dic13—212no—
160C4×Dic13—24no—
161C23×M16—131no—
162C23×M16—131no—
163C22×#117—131no—
164C2×#344—1312no—
165C23×C13—24no—
166C23×C13—24no—
167C23×C13—24no—
168C23×C13—46no—
169C23×C13—46no—
170C23×C13—46no—
171C23×C13—46no—
172C23×C13#9513yes—
173C23×C13#9513yes—
174C23×C13#9513yes—
175C23×C13#9516yes—
176C23×C13#9511yescharacteristic
177C23×C13C2×C4213yes—
178C23×C13C2×C4213yes—
179C23×C13C2×C22⋊C413yes—
180C23×C13C2×C22⋊C413yes—
181C23×C13C2×C4⋊C413yes—
182C23×C13C2×C4⋊C413yes—
183C23×C13C23×C411yescharacteristic
184C2×C4×C13—24no—
185C2×C4×C13—412no—
186C2×Dic13—24no—
187C2×Dic13—412no—
188C2×Dic13#9516yes—
189C2×Dic13#9516yes—
190C2×Dic13#9516yes—
191C2×Dic13#9516yes—
192C2×Dic13#9516yes—
193C2×Dic13#9516yes—
194C2×Dic13#9513yes—
195C2×Dic13#9513yes—
196C2×Dic13#9513yes—
197C2×Dic13#9513yes—
198C2×Dic13C2×C4213yes—
199C2×Dic13C2×C4213yes—
200C2×Dic13C2×C22⋊C413yes—
201C2×Dic13C2×C22⋊C413yes—
202C2×Dic13C2×C22⋊C413yes—
203C2×Dic13C2×C22⋊C413yes—
204C2×Dic13C2×C22⋊C413yes—
205C2×Dic13C2×C22⋊C413yes—
206C2×Dic13C2×C22⋊C413yes—
207C2×Dic13C2×C22⋊C413yes—
208C2×Dic13C2×C22⋊C413yes—
209C2×Dic13C2×C22⋊C413yes—
210C2×Dic13C2×C4⋊C413yes—
211C2×Dic13C2×C4⋊C413yes—
212C2×Dic13C2×C4⋊C413yes—
213C2×Dic13C2×C4⋊C413yes—
214C2×Dic13C2×C4⋊C413yes—
215C2×Dic13C2×C4⋊C413yes—
216C2×Dic13C2×C4⋊C413yes—
217C2×Dic13C2×C4⋊C413yes—
218C2×Dic13C2×C4⋊C413yes—
219C2×Dic13C2×C4⋊C413yes—
220C2×Dic13C23×C411yescharacteristic
221C2×Dic13C23×C411yescharacteristic
222C2×Dic13C22×D411yescharacteristic
223C2×Dic13C22×D411yescharacteristic
224C2×Dic13C22×D411yescharacteristic
225C2×Dic13C22×Q811yescharacteristic
226#1057—28no—
227#1057—28no—
228C24×C4—131no—
229C22×M16—136no—
230C22×M16—136no—
231C22×M16—136no—
232C22×M16—136no—
233C22×M16—132no—
234C22×M16—261no—
235C22×M16—263no—
236C22×M16—263no—
237C22×M16—261no—
238C22×M16—263no—
239C22×M16—261no—
240C22×M16—263no—
241C23×C8—132no—
242C23×C8—261no—
243C2×#117—136no—
244C2×#117—136no—
245C2×#117—263no—
246C2×#117—263no—
247C22×C4⋊C4—261no—
248C22×C22⋊C4—131no—
249C22×C22⋊C4#26111yescharacteristic
250C22×C42—261no—
251#344—1316no—
252C22×C13—26no—
253C22×C13—26no—
254C22×C13—26no—
255C22×C13—26no—
256C22×C13—26no—
257C22×C13—26no—
258C22×C13—46no—
259C22×C13—43no—
260C22×C13—43no—
261C22×C13—43no—
262C22×C13—41no—
263C22×C13#34414yescomplemented
264C22×C13C2×#9513yes—
265C22×C13C2×#9513yes—
266C22×C13C2×#9513yes—
267C22×C13C2×#9513yes—
268C22×C13C22×C4211yescharacteristic
269C22×C13C22×C22⋊C411yescharacteristic
270C22×C13C22×C4⋊C411yescharacteristic
271C4×C13—44no—
272Dic13—44no—
273Dic13C2×#9513yes—
274Dic13C2×#9513yes—
275Dic13C2×#9513yes—
276Dic13C2×#9513yes—
277Dic13C22×C22⋊C411yescharacteristic
278Dic13C22×C22⋊C411yescharacteristic
279Dic13C22×C4⋊C411yescharacteristic
280Dic13C22×C4⋊C411yescharacteristic
281C25C2×#26111yescharacteristic
282C23×C4—21no—
283C23×C4—131no—
284C23×C4—133no—
285C23×C4—133no—
286C23×C4—131no—
287C23×C4—131no—
288C23×C4—133no—
289C23×C4—133no—
290C23×C4—131no—
291C23×C4—131no—
292C23×C4—133no—
293C23×C4—133no—
294C23×C4—131no—
295C23×C4—133no—
296C23×C4—133no—
297C23×C4—261no—
298C2×M16—134no—
299C2×M16—1312no—
300C2×M16—134no—
301C2×M16—1312no—
302C2×M16—1312no—
303C2×M16—266no—
304C2×M16—266no—
305C2×M16—2612no—
306C2×M16—266no—
307C2×M16—266no—
308C2×M16—266no—
309C2×M16—266no—
310C2×M16—266no—
311C2×M16—266no—
312C2×M16—2612no—
313C2×M16—266no—
314C2×M16—266no—
315C2×M16—266no—
316C22×C8—1312no—
317C22×C8—266no—
318C22×C8—262no—
319C22×C8—266no—
320C22×C8—262no—
321C22×C8—266no—
322#117—1312no—
323#117—134no—
324#117—266no—
325#117—266no—
326#117—2612no—
327C2×C4⋊C4—266no—
328C2×C4⋊C4—266no—
329C2×C22⋊C4—23no—
330C2×C22⋊C4—136no—
331C2×C22⋊C4—263no—
332C2×C22⋊C4C2×#26116yes—
333C2×C42—266no—
334C2×C42—266no—
335C2×C13—21no—
336C2×C13—21no—
337C2×C13—23no—
338C2×C13—23no—
339C2×C13—23no—
340C2×C13—21no—
341C2×C13C2×#34416yescomplemented
342C2×C13C22×#9511yescharacteristic
343C24—44no—
344C24C4×#26111yescharacteristic
345C24C4×#26113yes—
346C24C4⋊#26111yescharacteristic
347C24C4⋊#26113yes—
348C24C22⋊#26111yescharacteristic
349C24C22⋊#26113yes—
350C24C22×#26113yes—
351C22×C4—26no—
352C22×C4—44no—
353C22×C4—133no—
354C22×C4—133no—
355C22×C4—133no—
356C22×C4—133no—
357C22×C4—133no—
358C22×C4—133no—
359C22×C4—136no—
360C22×C4—136no—
361C22×C4—133no—
362C22×C4—133no—
363C22×C4—133no—
364C22×C4—133no—
365C22×C4—133no—
366C22×C4—133no—
367C22×C4—136no—
368C22×C4—136no—
369C22×C4—131no—
370C22×C4—131no—
371C22×C4—131no—
372C22×C4—131no—
373C22×C4—133no—
374C22×C4—133no—
375C22×C4—133no—
376C22×C4—133no—
377C22×C4—133no—
378C22×C4—133no—
379C22×C4—136no—
380C22×C4—133no—
381C22×C4—133no—
382C22×C4—133no—
383C22×C4—133no—
384C22×C4—136no—
385C22×C4—133no—
386C22×C4—133no—
387C22×C4—133no—
388C22×C4—133no—
389C22×C4—133no—
390C22×C4—133no—
391C22×C4—133no—
392C22×C4—133no—
393C22×C4—136no—
394C22×C4—131no—
395C22×C4—133no—
396C22×C4—266no—
397C22×C4—524no—
398M16—138no—
399M16—264no—
400M16—264no—
401M16—2612no—
402M16—2612no—
403M16—264no—
404M16—2612no—
405M16—2612no—
406C2×C8—138no—
407C2×C8—2612no—
408C2×C8—2612no—
409C2×C8—264no—
410C2×C8—2612no—
411C2×C8—2612no—
412C4⋊C4—264no—
413C4⋊C4—2612no—
414C22⋊C4—26no—
415C22⋊C4—134no—
416C22⋊C4—266no—
417C22⋊C4C22×#26114yes—
418C42—264no—
419C42—2612no—
420C13C22×#34411yescharacteristic, complemented, Sylow
421C23—24no—
422C23—24no—
423C23—24no—
424C23—46no—
425C23—46no—
426C23—46no—
427C23—46no—
428C23(C2×#261)⋊C413yes—
429C23(C2×#261)⋊C413yes—
430C23(C2×#261)⋊C413yes—
431C23(C2×#261)⋊C416yes—
432C23(C2×#261)⋊C411yescharacteristic
433C23C2×C4×#26113yes—
434C23C2×C4×#26113yes—
435C23C2×C4⋊#26113yes—
436C23C2×C4⋊#26113yes—
437C23C2×C22⋊#26113yes—
438C23C2×C22⋊#26113yes—
439C23C23×#26111yescharacteristic
440C2×C4—24no—
441C2×C4—412no—
442C2×C4—131no—
443C2×C4—131no—
444C2×C4—133no—
445C2×C4—133no—
446C2×C4—131no—
447C2×C4—133no—
448C2×C4—133no—
449C2×C4—131no—
450C2×C4—131no—
451C2×C4—133no—
452C2×C4—131no—
453C2×C4—133no—
454C2×C4—133no—
455C2×C4—133no—
456C2×C4—133no—
457C2×C4—133no—
458C2×C4—133no—
459C2×C4—133no—
460C2×C4—133no—
461C2×C4—133no—
462C2×C4—136no—
463C2×C4—136no—
464C2×C4—136no—
465C2×C4—136no—
466C2×C4—136no—
467C2×C4—136no—
468C2×C4—133no—
469C2×C4—133no—
470C2×C4—133no—
471C2×C4—133no—
472C2×C4—133no—
473C2×C4—133no—
474C2×C4—133no—
475C2×C4—133no—
476C2×C4—133no—
477C2×C4—133no—
478C2×C4—133no—
479C2×C4—133no—
480C2×C4—264no—
481C2×C4—5212no—
482C8—268no—
483C8—268no—
484C22—26no—
485C22—26no—
486C22—26no—
487C22—26no—
488C22—26no—
489C22—26no—
490C22—46no—
491C22—43no—
492C22—43no—
493C22—43no—
494C22—41no—
495C22#1171823914yesdirect product factor
496C22C2×(C2×#261)⋊C413yes—
497C22C2×(C2×#261)⋊C413yes—
498C22C2×(C2×#261)⋊C413yes—
499C22C2×(C2×#261)⋊C413yes—
500C22C22×C4×#26111yescharacteristic
501C22C22×C4⋊#26111yescharacteristic
502C22C22×C22⋊#26111yescharacteristic
503C4—44no—
504C4—131no—
505C4—131no—
506C4—131no—
507C4—131no—
508C4—133no—
509C4—133no—
510C4—133no—
511C4—133no—
512C4—524no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—23no—
517C2—23no—
518C2—23no—
519C2C2×#1171823916yesdirect product factor
520C2C22×(C2×#261)⋊C411yescharacteristic
subgroupG/H
centerC23(C2×#261)⋊C4
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC22×C13×C22⋊C4C4
socleC23×C13#95
prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenterC22×C22⋊C4#261
hypocenterC13C22×#344
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#11718239C2direct (N × H)
13. C22×#6122C4semidirect
14. C22×#6122C4semidirect
15. C22×#6122C4semidirect
19. C23×#1057C4semidirect
28. #11718239C22direct (N × H)
59. C2×#6122C2×C4semidirect
60. C2×#6122C2×C4semidirect
61. C2×#6122C2×C4semidirect
69. C22×#1057C2×C4semidirect
146. #6122C22×C4semidirect
152. C2×#1057C22×C4semidirect
263. C22×C13#344semidirect
341. C2×C13C2×#344semidirect
420. C13C22×#344semidirect
495. C22#11718239direct (N × H)
519. C2C2×#11718239direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#61222
C2×#117182392
C22×#881312
C22×#34413