Finite Group Databasebeta

← C22×#11763690 #17968227

Subgroups — C22×#11763690 #17968227

Order 4352.

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×#63247C211yesmaximal, characteristic
2C23×#63247C211yesmaximal, characteristic
3C2×#11763690C2112yesmaximal, direct product factor
4C22×#10587563C211yesmaximal, characteristic
5C22×#63247—21no—
6C22×#63247—23no—
7C22×#63247—21no—
8C22×#63247—23no—
9C22×#63247—21no—
10C22×#63247—23no—
11C22×#63247—23no—
12C22×#63247C412yescomplemented
13C22×#63247C416yescomplemented
14C22×#63247C416yescomplemented
15C22×#63247C2216yes—
16C22×#63247C2216yes—
17C23×#3624—21no—
18C23×#3624C412yescomplemented
19#11763690C22116yesdirect product factor
20C24×Dic17C2211yescharacteristic
21C2×#10587563—23no—
22C2×#10587563—23no—
23C2×#10587563C416yes—
24C2×#10587563C2216yes—
25C22×#63225—21no—
26C22×C22⋊Dic17C411yescharacteristic
27C22×C4×Dic17—21no—
28C22×C22⋊C4×C17C411yescharacteristic
29C25×C17C2×C411yescharacteristic
30C23×C4×C17—21no—
31C23×Dic17—21no—
32C23×Dic17C2×C413yes—
33C23×Dic17C2×C411yescharacteristic
34C23×Dic17C2×C411yescharacteristic
35C23×Dic17C2×C413yes—
36C23×Dic17C2×C413yes—
37C23×Dic17D411yescharacteristic
38C23×Dic17D413yes—
39C23×Dic17D411yescharacteristic
40C23×Dic17D411yescharacteristic
41C23×Dic17D413yes—
42C23×Dic17D413yes—
43C23×Dic17Q811yescharacteristic
44C23×Dic17Q813yes—
45C23×Dic17C2313yes—
46C2×#63247—26no—
47C2×#63247—26no—
48C2×#63247—212no—
49C2×#63247—26no—
50C2×#63247—26no—
51C2×#63247—212no—
52C2×#63247—26no—
53C2×#63247—26no—
54C2×#63247—26no—
55C2×#63247—26no—
56C2×#63247—26no—
57C2×#63247—26no—
58C2×#63247—26no—
59C2×#63247C2×C4112yescomplemented
60C2×#63247C2×C4112yescomplemented
61C2×#63247C2×C4112yescomplemented
62C2×#63247C2314yes—
63C2×#63247C2314yes—
64C22×#3624—26no—
65C22×#3624—22no—
66C22×#3624—26no—
67C22×#3624—22no—
68C22×#3624—26no—
69C22×#3624C2×C4112yescomplemented
70C2×C22⋊C4×C17—23no—
71C2×C22⋊C4×C17C2×C416yes—
72C2×C22⋊Dic17—23no—
73C2×C22⋊Dic17C2×C416yes—
74C2×#63225—26no—
75C2×#63225—26no—
76C2×C4×Dic17—26no—
77C2×C4×Dic17—26no—
78#10587563—212no—
79#10587563—26no—
80#10587563—26no—
81#10587563C2×C4112yes—
82#10587563C2314yes—
83C24×C17—44no—
84C24×C17C4211yescharacteristic
85C24×C17C4213yes—
86C24×C17C22⋊C411yescharacteristic
87C24×C17C22⋊C413yes—
88C24×C17C4⋊C411yescharacteristic
89C24×C17C4⋊C413yes—
90C24×C17C22×C413yes—
91C22×C4×C17—26no—
92C22×C4×C17—44no—
93C22×Dic17—26no—
94C22×Dic17—44no—
95C22×Dic17C4213yes—
96C22×Dic17C4213yes—
97C22×Dic17C4216yes—
98C22×Dic17C22⋊C416yes—
99C22×Dic17C22⋊C413yes—
100C22×Dic17C22⋊C413yes—
101C22×Dic17C22⋊C413yes—
102C22×Dic17C22⋊C413yes—
103C22×Dic17C22⋊C411yescharacteristic
104C22×Dic17C22⋊C411yescharacteristic
105C22×Dic17C22⋊C413yes—
106C22×Dic17C22⋊C413yes—
107C22×Dic17C22⋊C413yes—
108C22×Dic17C22⋊C413yes—
109C22×Dic17C22⋊C416yes—
110C22×Dic17C22⋊C416yes—
111C22×Dic17C4⋊C413yes—
112C22×Dic17C4⋊C413yes—
113C22×Dic17C4⋊C416yes—
114C22×Dic17C4⋊C413yes—
115C22×Dic17C4⋊C413yes—
116C22×Dic17C4⋊C413yes—
117C22×Dic17C4⋊C413yes—
118C22×Dic17C4⋊C413yes—
119C22×Dic17C4⋊C413yes—
120C22×Dic17C4⋊C416yes—
121C22×Dic17C4⋊C416yes—
122C22×Dic17C4⋊C411yescharacteristic
123C22×Dic17C4⋊C411yescharacteristic
124C22×Dic17C22×C413yes—
125C22×Dic17C22×C413yes—
126C22×Dic17C22×C413yes—
127C22×Dic17C22×C413yes—
128C22×Dic17C22×C413yes—
129C22×Dic17C2×D413yes—
130C22×Dic17C2×D413yes—
131C22×Dic17C2×D413yes—
132C22×Dic17C2×D413yes—
133C22×Dic17C2×D413yes—
134C22×Dic17C2×D413yes—
135C22×Dic17C2×Q813yes—
136C22×Dic17C2×Q813yes—
137C22×Dic17C2411yescharacteristic
138#63247—212no—
139#63247—212no—
140#63247—212no—
141#63247—212no—
142#63247—24no—
143#63247—24no—
144#63247—24no—
145#63247C22×C418yescomplemented
146C2×#3624—212no—
147C2×#3624—212no—
148C2×#3624—212no—
149C2×#3624—212no—
150C2×#3624—24no—
151C2×#3624C22×C418yescomplemented
152C22⋊C4×C17—26no—
153C22⋊C4×C17C22×C414yes—
154C22⋊Dic17—26no—
155C22⋊Dic17C22×C414yes—
156#63225—212no—
157#63225—24no—
158C4×Dic17—212no—
159C4×Dic17—24no—
160C22×#344—171nomaximal, Sylow
161C23×C17—24no—
162C23×C17—24no—
163C23×C17—24no—
164C23×C17—46no—
165C23×C17—46no—
166C23×C17—46no—
167C23×C17—46no—
168C23×C17#9513yes—
169C23×C17#9513yes—
170C23×C17#9513yes—
171C23×C17#9516yes—
172C23×C17#9511yescharacteristic
173C23×C17C2×C4213yes—
174C23×C17C2×C4213yes—
175C23×C17C2×C22⋊C413yes—
176C23×C17C2×C22⋊C413yes—
177C23×C17C2×C4⋊C413yes—
178C23×C17C2×C4⋊C413yes—
179C23×C17C23×C411yescharacteristic
180C2×C4×C17—24no—
181C2×C4×C17—412no—
182C2×Dic17—24no—
183C2×Dic17—412no—
184C2×Dic17#9516yes—
185C2×Dic17#9516yes—
186C2×Dic17#9516yes—
187C2×Dic17#9516yes—
188C2×Dic17#9516yes—
189C2×Dic17#9516yes—
190C2×Dic17#9513yes—
191C2×Dic17#9513yes—
192C2×Dic17#9513yes—
193C2×Dic17#9513yes—
194C2×Dic17C2×C4213yes—
195C2×Dic17C2×C4213yes—
196C2×Dic17C2×C22⋊C413yes—
197C2×Dic17C2×C22⋊C413yes—
198C2×Dic17C2×C22⋊C413yes—
199C2×Dic17C2×C22⋊C413yes—
200C2×Dic17C2×C22⋊C413yes—
201C2×Dic17C2×C22⋊C413yes—
202C2×Dic17C2×C22⋊C413yes—
203C2×Dic17C2×C22⋊C413yes—
204C2×Dic17C2×C22⋊C413yes—
205C2×Dic17C2×C22⋊C413yes—
206C2×Dic17C2×C4⋊C413yes—
207C2×Dic17C2×C4⋊C413yes—
208C2×Dic17C2×C4⋊C413yes—
209C2×Dic17C2×C4⋊C413yes—
210C2×Dic17C2×C4⋊C413yes—
211C2×Dic17C2×C4⋊C413yes—
212C2×Dic17C2×C4⋊C413yes—
213C2×Dic17C2×C4⋊C413yes—
214C2×Dic17C2×C4⋊C413yes—
215C2×Dic17C2×C4⋊C413yes—
216C2×Dic17C23×C411yescharacteristic
217C2×Dic17C23×C411yescharacteristic
218C2×Dic17C22×D411yescharacteristic
219C2×Dic17C22×D411yescharacteristic
220C2×Dic17C22×D411yescharacteristic
221C2×Dic17C22×Q811yescharacteristic
222#3624—28no—
223#3624—28no—
224C23×M16—171no—
225C23×M16—171no—
226C22×#117—171no—
227C2×#344—1712no—
228C22×C17—26no—
229C22×C17—26no—
230C22×C17—26no—
231C22×C17—26no—
232C22×C17—26no—
233C22×C17—26no—
234C22×C17—46no—
235C22×C17—43no—
236C22×C17—43no—
237C22×C17—43no—
238C22×C17—41no—
239C22×C17#34414yescomplemented
240C22×C17C2×#9513yes—
241C22×C17C2×#9513yes—
242C22×C17C2×#9513yes—
243C22×C17C2×#9513yes—
244C22×C17C22×C4211yescharacteristic
245C22×C17C22×C22⋊C411yescharacteristic
246C22×C17C22×C4⋊C411yescharacteristic
247C4×C17—44no—
248Dic17—44no—
249Dic17C2×#9513yes—
250Dic17C2×#9513yes—
251Dic17C2×#9513yes—
252Dic17C2×#9513yes—
253Dic17C22×C22⋊C411yescharacteristic
254Dic17C22×C22⋊C411yescharacteristic
255Dic17C22×C4⋊C411yescharacteristic
256Dic17C22×C4⋊C411yescharacteristic
257C24×C4—171no—
258C22×M16—176no—
259C22×M16—176no—
260C22×M16—176no—
261C22×M16—172no—
262C22×M16—176no—
263C22×M16—341no—
264C22×M16—343no—
265C22×M16—343no—
266C22×M16—341no—
267C22×M16—343no—
268C22×M16—341no—
269C22×M16—343no—
270C23×C8—172no—
271C23×C8—341no—
272C2×#117—176no—
273C2×#117—176no—
274C2×#117—343no—
275C2×#117—343no—
276C22×C4⋊C4—341no—
277C22×C22⋊C4—171no—
278C22×C22⋊C4#59511yescharacteristic
279C22×C42—341no—
280#344—1716no—
281C2×C17—21no—
282C2×C17—21no—
283C2×C17—23no—
284C2×C17—23no—
285C2×C17—23no—
286C2×C17—21no—
287C2×C17C2×#34416yescomplemented
288C2×C17C22×#9511yescharacteristic
289C25C2×#59511yescharacteristic
290C23×C4—21no—
291C23×C4—171no—
292C23×C4—173no—
293C23×C4—173no—
294C23×C4—171no—
295C23×C4—171no—
296C23×C4—173no—
297C23×C4—173no—
298C23×C4—171no—
299C23×C4—171no—
300C23×C4—173no—
301C23×C4—173no—
302C23×C4—171no—
303C23×C4—173no—
304C23×C4—173no—
305C23×C4—341no—
306C2×M16—1712no—
307C2×M16—174no—
308C2×M16—1712no—
309C2×M16—1712no—
310C2×M16—174no—
311C2×M16—346no—
312C2×M16—346no—
313C2×M16—346no—
314C2×M16—346no—
315C2×M16—346no—
316C2×M16—346no—
317C2×M16—3412no—
318C2×M16—346no—
319C2×M16—346no—
320C2×M16—346no—
321C2×M16—346no—
322C2×M16—346no—
323C2×M16—3412no—
324C22×C8—1712no—
325C22×C8—346no—
326C22×C8—342no—
327C22×C8—346no—
328C22×C8—346no—
329C22×C8—342no—
330#117—174no—
331#117—1712no—
332#117—3412no—
333#117—346no—
334#117—346no—
335C2×C4⋊C4—346no—
336C2×C4⋊C4—346no—
337C2×C22⋊C4—23no—
338C2×C22⋊C4—176no—
339C2×C22⋊C4—343no—
340C2×C22⋊C4C2×#59516yes—
341C2×C42—346no—
342C2×C42—346no—
343C17C22×#34411yescharacteristic, complemented, Sylow
344C24—44no—
345C24C4×#59511yescharacteristic
346C24C4×#59513yes—
347C24C4⋊#59511yescharacteristic
348C24C4⋊#59513yes—
349C24C22⋊#59511yescharacteristic
350C24C22⋊#59513yes—
351C24C22×#59513yes—
352C22×C4—26no—
353C22×C4—44no—
354C22×C4—173no—
355C22×C4—173no—
356C22×C4—176no—
357C22×C4—173no—
358C22×C4—173no—
359C22×C4—173no—
360C22×C4—173no—
361C22×C4—173no—
362C22×C4—173no—
363C22×C4—176no—
364C22×C4—173no—
365C22×C4—173no—
366C22×C4—173no—
367C22×C4—173no—
368C22×C4—173no—
369C22×C4—173no—
370C22×C4—176no—
371C22×C4—173no—
372C22×C4—173no—
373C22×C4—173no—
374C22×C4—173no—
375C22×C4—173no—
376C22×C4—171no—
377C22×C4—173no—
378C22×C4—173no—
379C22×C4—173no—
380C22×C4—173no—
381C22×C4—173no—
382C22×C4—173no—
383C22×C4—176no—
384C22×C4—176no—
385C22×C4—173no—
386C22×C4—173no—
387C22×C4—173no—
388C22×C4—173no—
389C22×C4—173no—
390C22×C4—173no—
391C22×C4—176no—
392C22×C4—176no—
393C22×C4—171no—
394C22×C4—171no—
395C22×C4—171no—
396C22×C4—171no—
397C22×C4—346no—
398C22×C4—684no—
399M16—178no—
400M16—3412no—
401M16—3412no—
402M16—344no—
403M16—344no—
404M16—3412no—
405M16—3412no—
406M16—344no—
407C2×C8—178no—
408C2×C8—3412no—
409C2×C8—3412no—
410C2×C8—3412no—
411C2×C8—3412no—
412C2×C8—344no—
413C4⋊C4—344no—
414C4⋊C4—3412no—
415C22⋊C4—26no—
416C22⋊C4—174no—
417C22⋊C4—346no—
418C22⋊C4C22×#59514yes—
419C42—344no—
420C42—3412no—
421C23—24no—
422C23—24no—
423C23—24no—
424C23—46no—
425C23—46no—
426C23—46no—
427C23—46no—
428C23(C2×#595)⋊C413yes—
429C23(C2×#595)⋊C413yes—
430C23(C2×#595)⋊C413yes—
431C23(C2×#595)⋊C416yes—
432C23(C2×#595)⋊C411yescharacteristic
433C23C2×C4×#59513yes—
434C23C2×C4×#59513yes—
435C23C2×C4⋊#59513yes—
436C23C2×C4⋊#59513yes—
437C23C2×C22⋊#59513yes—
438C23C2×C22⋊#59513yes—
439C23C23×#59511yescharacteristic
440C2×C4—24no—
441C2×C4—412no—
442C2×C4—173no—
443C2×C4—173no—
444C2×C4—173no—
445C2×C4—173no—
446C2×C4—173no—
447C2×C4—173no—
448C2×C4—173no—
449C2×C4—173no—
450C2×C4—176no—
451C2×C4—176no—
452C2×C4—176no—
453C2×C4—176no—
454C2×C4—176no—
455C2×C4—176no—
456C2×C4—173no—
457C2×C4—173no—
458C2×C4—173no—
459C2×C4—173no—
460C2×C4—173no—
461C2×C4—173no—
462C2×C4—173no—
463C2×C4—173no—
464C2×C4—173no—
465C2×C4—173no—
466C2×C4—173no—
467C2×C4—173no—
468C2×C4—171no—
469C2×C4—171no—
470C2×C4—173no—
471C2×C4—173no—
472C2×C4—171no—
473C2×C4—173no—
474C2×C4—171no—
475C2×C4—173no—
476C2×C4—171no—
477C2×C4—173no—
478C2×C4—173no—
479C2×C4—171no—
480C2×C4—344no—
481C2×C4—6812no—
482C8—348no—
483C8—348no—
484C22—26no—
485C22—26no—
486C22—26no—
487C22—26no—
488C22—26no—
489C22—26no—
490C22—43no—
491C22—43no—
492C22—43no—
493C22—41no—
494C22—46no—
495C22#1176369014yesdirect product factor
496C22C2×(C2×#595)⋊C413yes—
497C22C2×(C2×#595)⋊C413yes—
498C22C2×(C2×#595)⋊C413yes—
499C22C2×(C2×#595)⋊C413yes—
500C22C22×C4×#59511yescharacteristic
501C22C22×C22⋊#59511yescharacteristic
502C22C22×C4⋊#59511yescharacteristic
503C4—44no—
504C4—171no—
505C4—171no—
506C4—171no—
507C4—171no—
508C4—173no—
509C4—173no—
510C4—173no—
511C4—173no—
512C4—684no—
513C2—21no—
514C2—23no—
515C2—23no—
516C2—23no—
517C2—21no—
518C2—21no—
519C2C2×#1176369016yesdirect product factor
520C2C22×(C2×#595)⋊C411yescharacteristic
subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17#95
prime radicalC25×C17C2×C4
cosocleC22×Dic17C24
hypercenterC22×C22⋊C4#595
hypocenterC17C22×#344
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#11763690C2direct (N × H)
12. C22×#63247C4semidirect
13. C22×#63247C4semidirect
14. C22×#63247C4semidirect
18. C23×#3624C4semidirect
19. #11763690C22direct (N × H)
59. C2×#63247C2×C4semidirect
60. C2×#63247C2×C4semidirect
61. C2×#63247C2×C4semidirect
69. C22×#3624C2×C4semidirect
145. #63247C22×C4semidirect
151. C2×#3624C22×C4semidirect
239. C22×C17#344semidirect
287. C2×C17C2×#344semidirect
343. C17C22×#344semidirect
495. C22#11763690direct (N × H)
519. C2C2×#11763690direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#632472
C2×#117636902
C22×#105875632
C22×#34417