Finite Group Databasebeta

← #17964327

Subgroups — #17964327

Order 4352.

1210 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#14545639C212yesmaximal, complemented
2#14544047C212yesmaximal, complemented
3#14544041C212yesmaximal, complemented
4#14544037C212yesmaximal, complemented
5#14544033C212yesmaximal, complemented
6#14544021C212yesmaximal, complemented
7#14544013C212yesmaximal, complemented
8C2×#11763291C211yesmaximal, characteristic
9#11763839—28no—
10#11763829C2214yes—
11#11763780C2214yes—
12#11763777C2214yes—
13#11763655C2214yes—
14#11763654C2214yes—
15#11763654C2214yes—
16#11763653C2214yes—
17C22×#63256C411yescharacteristic
18#11763291—28no—
19C2×Q8×Dic17C2211yescharacteristic
20C2×C4×D68C411yescharacteristic
21C2×C4×D68C2211yescharacteristic
22C2×C4×D68C2211yescharacteristic
23C2×#10587579C411yescharacteristic
24C2×#10587579C411yescharacteristic
25C2×#10587579C2211yescharacteristic
26C2×#10587558C411yescharacteristic
27C2×#10587558C411yescharacteristic
28C2×#10587558C2211yescharacteristic
29C2×C4⋊C4×D17C411yescharacteristic
30C2×C4⋊C4×D17C2211yescharacteristic
31C2×C4⋊C4×D17C2211yescharacteristic
32C2×C4×Q8×C17C411yescharacteristic
33C22×Q8×C17C2×C411yescharacteristic
34C2×#63256—24no—
35C2×#63256—24no—
36C2×#63256—24no—
37C22×D68C2×C411yescharacteristic
38C22×D68C2×C411yescharacteristic
39C22×D68C2×C411yescharacteristic
40C22×C4×D17C2×C411yescharacteristic
41C22×C4×D17C2×C411yescharacteristic
42C22×C4×D17C2×C411yescharacteristic
43C22×C4×D17C2×C411yescharacteristic
44C22×C4×D17C2×C411yescharacteristic
45C22×C4×D17C2×C411yescharacteristic
46C22×C4×D17C2×C411yescharacteristic
47C22×C4×D17C2311yescharacteristic
48C22×C4×D17C2311yescharacteristic
49C2×#63243—24no—
50C2×#63242—24no—
51C4×Q8×C17—24no—
52C2×C4⋊C4×C17C2×C411yescharacteristic
53C2×C4⋊C4×C17C2×C411yescharacteristic
54C2×C4⋊C4×C17C2×C411yescharacteristic
55C2×C42×C17C2×C411yescharacteristic
56C2×C42×C17C2×C411yescharacteristic
57C2×C42×C17C2×C411yescharacteristic
58Q8×Dic17—24no—
59C2×#63227C2×C411yescharacteristic
60C2×#63227C2×C411yescharacteristic
61C2×#63227C2×C411yescharacteristic
62C2×#63227C2×C411yescharacteristic
63C2×#63227C2×C411yescharacteristic
64C2×#63227C2311yescharacteristic
65C2×C4⋊Dic17C2×C411yescharacteristic
66C2×C4⋊Dic17C2311yescharacteristic
67C2×C4⋊Dic17C2311yescharacteristic
68C2×#63225C2×C411yescharacteristic
69C2×#63225C2×C411yescharacteristic
70C2×#63225C2×C411yescharacteristic
71C2×#63225C2311yescharacteristic
72C2×C4×Dic17C2×C411yescharacteristic
73C2×C4×Dic17C2×C411yescharacteristic
74C2×C4×Dic17C2311yescharacteristic
75#10587579—24no—
76#10587579—24no—
77#10587579D418yes—
78C4⋊C4×D17—24no—
79C4⋊C4×D17—24no—
80C4⋊C4×D17—24no—
81C4×D68—24no—
82C4×D68—24no—
83C4×D68—24no—
84#10587558—24no—
85#10587558—24no—
86#10587558—24no—
87C22⋊#3624C2318yes—
88#10587544—24no—
89#10587543—24no—
90#10587543—24no—
91#10587542—24no—
92C23×D17C22×C411yescharacteristic
93C23×D17C22×C411yescharacteristic
94C23×D17C22×C411yescharacteristic
95C2×Q8×C17—22no—
96C2×Q8×C17—22no—
97C2×Q8×C17—22no—
98C22×C4×C17C22×C411yescharacteristic
99C22×C4×C17C22×C411yescharacteristic
100C22×C4×C17C22×C411yescharacteristic
101C22×C4×C17C22×C411yescharacteristic
102C22×C4×C17C22×C411yescharacteristic
103C22×C4×C17C22×C411yescharacteristic
104C22×C4×C17C22×C411yescharacteristic
105C22×Dic17C22×C411yescharacteristic
106C22×Dic17C22×C411yescharacteristic
107C22×Dic17C22×C411yescharacteristic
108C22×Dic17C22×C411yescharacteristic
109C22×Dic17C2411yescharacteristic
110#63256—232no—
111C2×D68—22no—
112C2×D68—22no—
113C2×D68—22no—
114C2×D68—22no—
115C2×D68—22no—
116C2×D68—22no—
117C2×D68—22no—
118C2×D68C22⋊C414yes—
119C2×D68M1614yescomplemented
120C2×C4×D17—22no—
121C2×C4×D17—22no—
122C2×C4×D17—22no—
123C2×C4×D17—22no—
124C2×C4×D17—22no—
125C2×C4×D17—22no—
126C2×C4×D17—22no—
127C2×C4×D17—22no—
128C2×C4×D17—22no—
129C2×C4×D17—22no—
130C2×C4×D17—22no—
131C2×C4×D17—22no—
132C2×C4×D17—81no—
133C2×C4×D17—81no—
134C2×C4×D17—81no—
135C2×C4×D17—81no—
136C2×C4×D17—81no—
137C2×C4×D17—81no—
138C2×C4×D17M1614yescomplemented
139C2×C4×D17C2×D414yes—
140C2×C4×D17C2×D414yes—
141C2×#3624—28no—
142#63243—84no—
143#63242—84no—
144C4⋊C4×C17—22no—
145C4⋊C4×C17—22no—
146C4⋊C4×C17C22⋊C414yes—
147C42×C17—22no—
148C42×C17—22no—
149C42×C17—22no—
150#63227—22no—
151#63227—22no—
152#63227—22no—
153#63227—22no—
154#63227C22⋊C414yes—
155#63227C22⋊C414yes—
156C4⋊Dic17—22no—
157C4⋊Dic17—22no—
158C4⋊Dic17—22no—
159#63225—22no—
160#63225—22no—
161#63225—22no—
162#63225—22no—
163C4×Dic17—22no—
164C4×Dic17—22no—
165C4×Dic17C2×D414yes—
166#17368—171nomaximal, Sylow
167C23×C17C23×C411yescharacteristic
168C22×D17—21no—
169C22×D17—21no—
170C22×D17—21no—
171C22×D17—21no—
172C22×D17—41no—
173C22×D17—41no—
174C22×D17—41no—
175C22×D17—41no—
176C22×D17—41no—
177C22×D17—41no—
178C22×D17C2×C22⋊C412yes—
179C22×D17C2×C22⋊C412yes—
180C22×D17C2×M1612yes—
181C22×D17C2×M1612yes—
182C22×D17C2×M1612yes—
183Q8×C17—28no—
184C2×C4×C17—21no—
185C2×C4×C17—21no—
186C2×C4×C17—21no—
187C2×C4×C17—21no—
188C2×C4×C17—21no—
189C2×C4×C17—21no—
190C2×C4×C17—21no—
191C2×C4×C17—21no—
192C2×C4×C17—41no—
193C2×C4×C17—41no—
194C2×C4×C17—41no—
195C2×C4×C17—41no—
196C2×C4×C17C2×C22⋊C412yes—
197C2×C4×C17C2×C22⋊C412yes—
198C2×C4×C17C2×C22⋊C412yes—
199C2×C4×C17C2×M1612yes—
200C2×C4×C17C2×M1612yes—
201C2×Dic17—21no—
202C2×Dic17—21no—
203C2×Dic17—21no—
204C2×Dic17—21no—
205C2×Dic17—41no—
206C2×Dic17—41no—
207C2×Dic17—41no—
208C2×Dic17—41no—
209C2×Dic17C2×C22⋊C412yes—
210C2×Dic17C2×M1612yes—
211C2×Dic17C22×D412yes—
212D68—28no—
213D68—28no—
214D68—28no—
215C4×D17—28no—
216C4×D17—28no—
217C4×D17—28no—
218C4×D17—44no—
219C4×D17—44no—
220C4×D17—82no—
221C4×D17—82no—
222C4×D17—82no—
223C4×D17—82no—
224#3624—48no—
225C2×#520—171no—
226#2973—172no—
227#1467—172no—
228#1465—172no—
229#1464—172no—
230#1463—172no—
231#1459—172no—
232C2×#324—172no—
233C22×C17—21no—
234C22×C17—21no—
235C22×C17C22×C22⋊C411yescharacteristic
236C22×C17C22×M1611yescharacteristic
237C22×C17C22×M1611yescharacteristic
238C2×D17—22no—
239C2×D17—22no—
240C2×D17—22no—
241C2×D17—22no—
242C2×D17—22no—
243C2×D17—22no—
244C2×D17—42no—
245C2×D17—42no—
246C2×D17—42no—
247C2×D17—42no—
248C2×D17—42no—
249C2×D17—41no—
250C2×D17—41no—
251C2×D17—42no—
252C2×D17#40714yes—
253C4×C17—22no—
254C4×C17—22no—
255C4×C17—22no—
256C4×C17—22no—
257C4×C17—22no—
258C4×C17—41no—
259C4×C17—41no—
260Dic17—22no—
261Dic17—22no—
262Dic17—22no—
263Dic17—41no—
264Dic17—41no—
265C22×#41—171no—
266#520—348no—
267C2×C4×Q8—171no—
268C2×C4×Q8#59511yescharacteristic
269C2×C4×D4—171no—
270C2×C4×D4—171no—
271C2×C4×D4—171no—
272C2×C4×D4—171no—
273C2×C4×D4—171no—
274C2×C4×D4—171no—
275C2×#117—171no—
276C2×#117—171no—
277C2×#117—171no—
278C22×C4⋊C4—171no—
279C22×C4⋊C4—171no—
280C22×C4⋊C4—171no—
281#435—348no—
282#432—174no—
283#407—174no—
284C2×C22⋊C8—174no—
285#324—174no—
286#324—174no—
287#324—174no—
288#323—174no—
289C2×C17—21no—
290C2×C17—21no—
291C2×C17C2×#40711yescharacteristic
292C2×C17#288311yescharacteristic
293C2×C17#288911yescharacteristic
294D17—24no—
295D17—42no—
296D17—42no—
297C2×#41—344no—
298C2×#41—344no—
299C2×#41—344no—
300C22×Q8C2×#59511yescharacteristic
301C22×D4—171no—
302C22×D4—171no—
303C22×D4—171no—
304C23×C4—171no—
305C23×C4—171no—
306C23×C4—171no—
307C23×C4—171no—
308C23×C4—171no—
309C23×C4—171no—
310C23×C4—171no—
311C23×C4—171no—
312C23×C4—171no—
313C2×M16—344no—
314C22×C8—344no—
315C4×Q8—24no—
316C4×Q8—344no—
317C4×D4—178no—
318C4×D4—344no—
319C4×D4—344no—
320C4×D4—344no—
321C4×D4—344no—
322C4×D4—344no—
323#117—344no—
324#117—344no—
325#117—344no—
326C2×C4⋊C4—171no—
327C2×C4⋊C4—171no—
328C2×C4⋊C4—171no—
329C2×C4⋊C4—171no—
330C2×C4⋊C4—171no—
331C2×C4⋊C4—171no—
332C2×C4⋊C4—171no—
333C2×C4⋊C4—344no—
334C2×C4⋊C4—344no—
335C2×C4⋊C4—344no—
336C2×C4⋊C4C2×#59511yescharacteristic
337C2×C4⋊C4C2×#59511yescharacteristic
338C2×C4⋊C4C2×#59511yescharacteristic
339C2×C22⋊C4—171no—
340C2×C22⋊C4—171no—
341C2×C22⋊C4—171no—
342C2×C22⋊C4—171no—
343C2×C22⋊C4—171no—
344C2×C22⋊C4—171no—
345C2×C42—171no—
346C2×C42—171no—
347C2×C42—171no—
348C2×C42C2×#59511yescharacteristic
349C2×C42C2×#59511yescharacteristic
350C2×C42C2×#59511yescharacteristic
351C4⋊C8—344no—
352C22⋊C8—178no—
353C22⋊C8—344no—
354C22⋊C8—344no—
355#97—344no—
356C17#1736811yescharacteristic, complemented, Sylow
357C24—171no—
358C24—171no—
359C24—171no—
360#41—3432no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×D4—174no—
365C2×D4—174no—
366C2×D4—342no—
367C2×D4—342no—
368C2×D4—342no—
369C2×D4—342no—
370C2×D4—342no—
371C2×D4—342no—
372C2×D4—342no—
373C22×C4—171no—
374C22×C4—171no—
375C22×C4—171no—
376C22×C4—174no—
377C22×C4—174no—
378C22×C4—174no—
379C22×C4—171no—
380C22×C4—171no—
381C22×C4—342no—
382C22×C4—342no—
383C22×C4—342no—
384C22×C4—342no—
385C22×C4—342no—
386C22×C4—342no—
387C22×C4—342no—
388C22×C4—342no—
389C22×C4—342no—
390C22×C4—342no—
391C22×C4—342no—
392C22×C4—342no—
393C22×C4—1361no—
394C22×C4—1361no—
395C22×C4—1361no—
396C22×C4—1361no—
397C22×C4—1361no—
398C22×C4—1361no—
399C22×C4C22×#59511yescharacteristic
400C22×C4C22×#59511yescharacteristic
401C22×C4C22×#59511yescharacteristic
402C22×C4C22×#59511yescharacteristic
403C22×C4C22×#59511yescharacteristic
404C22×C4C22×#59511yescharacteristic
405C22×C4C22×#59511yescharacteristic
406M16—1364no—
407C2×C8—348no—
408C2×C8—1364no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—342no—
412C4⋊C4—342no—
413C4⋊C4—342no—
414C4⋊C4—342no—
415C4⋊C4—342no—
416C4⋊C4—342no—
417C4⋊C4—342no—
418C4⋊C4C22⋊#59514yes—
419C22⋊C4—174no—
420C22⋊C4—174no—
421C22⋊C4—342no—
422C22⋊C4—342no—
423C22⋊C4—342no—
424C22⋊C4—342no—
425C42—22no—
426C42—22no—
427C42—22no—
428C42—174no—
429C42—342no—
430C42—342no—
431C23—172no—
432C23—172no—
433C23—172no—
434C23—172no—
435C23—172no—
436C23—341no—
437C23—341no—
438C23—341no—
439C23—341no—
440C23—681no—
441C23—681no—
442C23—681no—
443C23—681no—
444C23—681no—
445C23—681no—
446C23C23×#59511yescharacteristic
447Q8—28no—
448D4—348no—
449D4—348no—
450D4—348no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—172no—
464C2×C4—172no—
465C2×C4—172no—
466C2×C4—348no—
467C2×C4—348no—
468C2×C4—348no—
469C2×C4—341no—
470C2×C4—341no—
471C2×C4—341no—
472C2×C4—341no—
473C2×C4—684no—
474C2×C4—684no—
475C2×C4—681no—
476C2×C4—681no—
477C2×C4—681no—
478C2×C4—681no—
479C2×C4—1362no—
480C2×C4—1362no—
481C2×C4—1362no—
482C2×C4—1362no—
483C2×C4D17⋊M1612yes—
484C2×C4D17⋊M1612yes—
485C2×C4C2×C22⋊#59512yes—
486C2×C4C2×C22⋊#59512yes—
487C2×C4C2×C22⋊#59512yes—
488C8—688no—
489C22—21no—
490C22—21no—
491C22—174no—
492C22—342no—
493C22—342no—
494C22—342no—
495C22—342no—
496C22—342no—
497C22—342no—
498C22—682no—
499C22—682no—
500C22—682no—
501C22—682no—
502C22—682no—
503C22—682no—
504C22—681no—
505C22—681no—
506C22C22×C22⋊#59511yescharacteristic
507C22C2×D17⋊M1611yescharacteristic
508C22C2×D17⋊M1611yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—22no—
513C4—22no—
514C4—41no—
515C4—41no—
516C4—342no—
517C4—342no—
518C4—342no—
519C4—681no—
520C4—681no—
521C2—21no—
522C2—21no—
523C2—344no—
524C2—682no—
525C2—682no—
526C2D17⋊#40711yescharacteristic
527C2#1454538411yescharacteristic
528C2#1454539711yescharacteristic
subgroupG/H
centerC22C22×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC2×C4×Q8×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC22×#63256C4
cosocleC22×Dic17C24
hypercenterC2×C4×Q8#595
hypocenterC17#17368
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14545639C2semidirect
2. #14544047C2semidirect
3. #14544041C2semidirect
4. #14544037C2semidirect
5. #14544033C2semidirect
6. #14544021C2semidirect
7. #14544013C2semidirect
119. C2×D68M16semidirect
138. C2×C4×D17M16semidirect
356. C17#17368semidirect

Maximal subgroups

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

subgroupindex
#145456392
#145440472
#145440412
#145440372
#145440332
#145440212
#145440132
C2×#117632912
#1736817