Finite Group Databasebeta

← #17956937

Subgroups — #17956937

Order 4352.

1194 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763687C212yesmaximal
2C2×#11763687C212yesmaximal
3#14543958C212yesmaximal
4C2×C4×#63227C211yesmaximal, characteristic
5C22×C22⋊#595C2214yes—
6C2×(C2×#595)⋊C4—22no—
7C2×(C2×#595)⋊C4—22no—
8#11763687—24no—
9#11763687C418yescomplemented
10C23×C4×D17C2211yescharacteristic
11C22×#63227C2211yescharacteristic
12C22×#63227C2211yescharacteristic
13C22×C4×Dic17C411yescharacteristic, complemented
14C4×#63227—22no—
15C4×#63227—22no—
16C2×#10587502C411yescharacteristic, complemented
17C2×#10587502C411yescharacteristic, complemented
18C22×C42×C17C411yescharacteristic, complemented
19C24×D17C2311yescharacteristic
20C23×#595—24no—
21C23×C4×C17C2×C411yescharacteristic
22C23×C4×C17C2×C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17C2×C411yescharacteristic
25C23×Dic17C2×C411yescharacteristic
26C23×Dic17C2×C411yescharacteristic
27C22×C4×D17—22no—
28C22×C4×D17—22no—
29C22×C4×D17—42no—
30C22×C4×D17—42no—
31C22×C4×D17D412yes—
32C22×C4×D17D412yes—
33C2×C22⋊#595—24no—
34C2×C22⋊#595—24no—
35C2×C22⋊#595—24no—
36C2×C22⋊#595—24no—
37C2×C22⋊#595—24no—
38C2×C22⋊#595C2×C418yes—
39C2×C42×C17—21no—
40C2×C42×C17—21no—
41C2×C42×C17—42no—
42C2×#63227—22no—
43C2×#63227—22no—
44C2×#63227—22no—
45C2×#63227—22no—
46C2×#63227C2×C414yes—
47C2×#63227D412yes—
48C2×#63227Q812yes—
49C2×C4×Dic17—21no—
50C2×C4×Dic17—21no—
51C2×C4×Dic17—42no—
52(C2×#595)⋊C4—44no—
53(C2×#595)⋊C4—44no—
54#10587502—22no—
55#10587502—22no—
56C24×C17C22×C411yescharacteristic
57C23×D17—41no—
58C23×D17—41no—
59C23×D17—41no—
60C23×D17—41no—
61C23×D17C22×C412yes—
62C23×D17C2×D412yes—
63C23×D17C2×D411yescharacteristic
64C23×D17C2×Q811yescharacteristic
65C23×D17#4112yes—
66C23×D17#4112yes—
67C23×D17#4112yes—
68C23×D17#4112yes—
69C22×#595—28no—
70C22×#595—44no—
71C22×#595—44no—
72C22×#595—44no—
73C22×#595—44no—
74C22×#595—44no—
75C22×#595—44no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—22no—
79C22×C4×C17—22no—
80C22×C4×C17—21no—
81C22×C4×C17—21no—
82C22×C4×C17—21no—
83C22×C4×C17—21no—
84C22×C4×C17—41no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17—41no—
88C22×C4×C17C4212yes—
89C22×C4×C17C22⋊C411yescharacteristic
90C22×C4×C17C22⋊C411yescharacteristic
91C22×C4×C17C4⋊C412yes—
92C22×Dic17—21no—
93C22×Dic17—21no—
94C22×Dic17—21no—
95C22×Dic17—21no—
96C22×Dic17—21no—
97C22×Dic17—21no—
98C22×Dic17—41no—
99C22×Dic17—41no—
100C22×Dic17—41no—
101C22×Dic17—41no—
102C22×Dic17—41no—
103C22×Dic17—41no—
104C22×Dic17C4212yes—
105C22×Dic17C22⋊C412yes—
106C22×Dic17C4⋊C412yes—
107C2×C4×D17—24no—
108C2×C4×D17—24no—
109C2×C4×D17—24no—
110C2×C4×D17—24no—
111C2×C4×D17—42no—
112C2×C4×D17—42no—
113C2×C4×D17—48no—
114C2×C4×D17—48no—
115C22⋊#595—28no—
116C22⋊#595—28no—
117C22⋊#595—44no—
118C22⋊#595—44no—
119C42×C17—42no—
120C42×C17—42no—
121#63227—28no—
122#63227—24no—
123#63227—24no—
124C4×Dic17—42no—
125C4×Dic17—42no—
126#10801—171nomaximal, Sylow
127C23×C17—21no—
128C23×C17—21no—
129C23×C17—21no—
130C23×C17—21no—
131C23×C17C2×C4211yescharacteristic
132C23×C17C2×C22⋊C411yescharacteristic
133C23×C17C2×C4⋊C411yescharacteristic
134C23×C17#11711yescharacteristic
135C23×C17#11711yescharacteristic
136C23×C17#11711yescharacteristic
137C23×C17#11711yescharacteristic
138C22×D17—22no—
139C22×D17—22no—
140C22×D17—22no—
141C22×D17—22no—
142C22×D17—42no—
143C22×D17—42no—
144C22×D17—42no—
145C22×D17—42no—
146C22×D17—41no—
147C22×D17—41no—
148C22×D17—41no—
149C22×D17—41no—
150C22×D17—42no—
151C22×D17—42no—
152C22×D17—42no—
153C22×D17—42no—
154C22×D17—42no—
155C22×D17—42no—
156C22×D17#11714yes—
157C22×D17C4×D414yes—
158C22×D17C4×D412yes—
159C22×D17C4×Q812yes—
160C22×D17#12112yes—
161C22×D17C22⋊Q812yes—
162C22×D17#12314yes—
163C22×D17#12412yes—
164C22×D17#12512yes—
165C22×D17#12614yes—
166C2×#595—48no—
167C2×#595—48no—
168C2×#595—48no—
169C2×#595—84no—
170C2×#595—84no—
171C2×#595—84no—
172C2×#595—84no—
173C2×C4×C17—24no—
174C2×C4×C17—24no—
175C2×C4×C17—21no—
176C2×C4×C17—21no—
177C2×C4×C17—21no—
178C2×C4×C17—21no—
179C2×C4×C17—22no—
180C2×C4×C17—22no—
181C2×C4×C17—42no—
182C2×C4×C17—42no—
183C2×C4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—41no—
186C2×C4×C17—41no—
187C2×C4×C17—42no—
188C2×C4×C17—42no—
189C2×C4×C17#9912yes—
190C2×C4×C17#9912yes—
191C2×Dic17—22no—
192C2×Dic17—22no—
193C2×Dic17—22no—
194C2×Dic17—22no—
195C2×Dic17—22no—
196C2×Dic17—42no—
197C2×Dic17—42no—
198C2×Dic17—42no—
199C2×Dic17—42no—
200C2×Dic17—41no—
201C2×Dic17—41no—
202C2×Dic17—41no—
203C2×Dic17—41no—
204C2×Dic17—42no—
205C2×Dic17—42no—
206C4×D17—48no—
207C4×D17—48no—
208C2×C4×C22⋊C4—171no—
209C2×#342—172no—
210C2×#342—172no—
211C22⋊#95—172no—
212C22×C17—21no—
213C22×C17—21no—
214C22×C17—21no—
215C22×C17—21no—
216C22×C17—21no—
217C22×C17—21no—
218C22×C17—21no—
219C22×C17—21no—
220C22×C17—21no—
221C22×C17—21no—
222C22×C17—21no—
223C22×C17—21no—
224C22×C17#37611yescharacteristic
225C22×C17C4×C22⋊C411yescharacteristic
226C22×C17C4×C4⋊C411yescharacteristic
227C22×C17#38011yescharacteristic
228C22×C17#38111yescharacteristic
229C22×C17#38211yescharacteristic
230C22×C17#38311yescharacteristic
231C22×C17C2×#9911yescharacteristic
232C22×C17C2×#9911yescharacteristic
233C22×C17#41011yescharacteristic
234C22×C17#41011yescharacteristic
235C2×D17—22no—
236C2×D17—22no—
237C2×D17—22no—
238C2×D17—22no—
239C2×D17—24no—
240C2×D17—24no—
241C2×D17—24no—
242C2×D17—24no—
243C2×D17—44no—
244C2×D17—42no—
245C2×D17—42no—
246C2×D17—42no—
247C2×D17—42no—
248C2×D17—44no—
249C2×D17#38714yes—
250C2×D17#38814yes—
251#595—88no—
252C4×C17—22no—
253C4×C17—22no—
254C4×C17—42no—
255C4×C17—42no—
256Dic17—42no—
257Dic17—42no—
258Dic17—42no—
259C24×C4—171no—
260C22×C22⋊C4—171no—
261C22×C22⋊C4—171no—
262C22×C22⋊C4—174no—
263C22×C42—171no—
264C22×C42#59511yescharacteristic, complemented
265C4×C22⋊C4—342no—
266C4×C22⋊C4—342no—
267C2×#95—171no—
268C2×#95—171no—
269C2×#95—342no—
270C2×#95—342no—
271#342—178no—
272#342—344no—
273C2×C17—21no—
274C2×C17—21no—
275C2×C17—21no—
276C2×C17—21no—
277C2×C17#143411yescharacteristic
278C2×C17C4×#9911yescharacteristic
279C2×C17C4×#9911yescharacteristic
280C2×C17#179911yescharacteristic
281C2×C17#179911yescharacteristic
282C2×C17#181911yescharacteristic
283C2×C17#182011yescharacteristic
284D17—24no—
285D17—24no—
286C25—171no—
287C23×C4—171no—
288C23×C4—171no—
289C23×C4—171no—
290C23×C4—172no—
291C23×C4—172no—
292C23×C4—342no—
293C23×C4—342no—
294C23×C4—344no—
295C23×C4—682no—
296C23×C4—682no—
297C23×C4C2×#59511yescharacteristic
298C23×C4C2×#59511yescharacteristic
299C23×C4C2×#59511yescharacteristic
300C2×C22⋊C4—174no—
301C2×C22⋊C4—172no—
302C2×C22⋊C4—172no—
303C2×C22⋊C4—178no—
304C2×C22⋊C4—342no—
305C2×C22⋊C4—342no—
306C2×C22⋊C4—342no—
307C2×C22⋊C4—342no—
308C2×C22⋊C4—344no—
309C2×C22⋊C4—344no—
310C2×C22⋊C4—344no—
311C2×C22⋊C4—344no—
312C2×C22⋊C4—344no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—42no—
316C2×C42—341no—
317C2×C42—341no—
318C2×C42—682no—
319#95—342no—
320#95—342no—
321#95—684no—
322#95—684no—
323C17#1080111yescharacteristic, complemented, Sylow
324C24—172no—
325C24—172no—
326C24—171no—
327C24—171no—
328C24—172no—
329C24—172no—
330C24—172no—
331C24—172no—
332C24—681no—
333C24—681no—
334C24—681no—
335C24—681no—
336C24C22×#59511yescharacteristic
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—172no—
350C22×C4—172no—
351C22×C4—172no—
352C22×C4—344no—
353C22×C4—344no—
354C22×C4—341no—
355C22×C4—341no—
356C22×C4—341no—
357C22×C4—341no—
358C22×C4—341no—
359C22×C4—341no—
360C22×C4—344no—
361C22×C4—344no—
362C22×C4—348no—
363C22×C4—682no—
364C22×C4—682no—
365C22×C4—688no—
366C22×C4—688no—
367C22×C4—681no—
368C22×C4—681no—
369C22×C4—681no—
370C22×C4—681no—
371C22×C4—681no—
372C22×C4—681no—
373C22×C4—684no—
374C22×C4—684no—
375C22×C4—684no—
376C22×C4—684no—
377C22×C4—684no—
378C22×C4—684no—
379C22×C4C4×#59512yes—
380C22×C4C4⋊#59512yes—
381C22×C4C22⋊#59511yescharacteristic
382C22×C4C22⋊#59511yescharacteristic
383C22⋊C4—348no—
384C22⋊C4—344no—
385C22⋊C4—344no—
386C22⋊C4—348no—
387C22⋊C4—348no—
388C22⋊C4—684no—
389C22⋊C4—684no—
390C42—42no—
391C42—42no—
392C42—682no—
393C42—682no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—174no—
399C23—172no—
400C23—172no—
401C23—174no—
402C23—174no—
403C23—172no—
404C23—172no—
405C23—172no—
406C23—172no—
407C23—174no—
408C23—342no—
409C23—342no—
410C23—342no—
411C23—342no—
412C23—682no—
413C23—682no—
414C23—681no—
415C23—681no—
416C23—682no—
417C23—681no—
418C23—681no—
419C23—682no—
420C23—682no—
421C23—682no—
422C23—682no—
423C23—682no—
424C23—682no—
425C23—682no—
426C23C2×C4×#59511yescharacteristic
427C23C2×C4⋊#59511yescharacteristic
428C23#1058767711yescharacteristic
429C23#1058767711yescharacteristic
430C23#1058767711yescharacteristic
431C23#1058767711yescharacteristic
432C23C2×C22⋊#59511yescharacteristic
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—342no—
450C2×C4—342no—
451C2×C4—342no—
452C2×C4—342no—
453C2×C4—342no—
454C2×C4—688no—
455C2×C4—688no—
456C2×C4—682no—
457C2×C4—682no—
458C2×C4—682no—
459C2×C4—682no—
460C2×C4—681no—
461C2×C4—681no—
462C2×C4—681no—
463C2×C4—681no—
464C2×C4—682no—
465C2×C4—682no—
466C2×C4—688no—
467C2×C4—688no—
468C2×C4—688no—
469C2×C4—1364no—
470C2×C4—1364no—
471C2×C4—1364no—
472C2×C4—1364no—
473C2×C4#1058753912yes—
474C2×C4#1058755112yes—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—174no—
488C22—174no—
489C22—342no—
490C22—342no—
491C22—342no—
492C22—342no—
493C22—344no—
494C22—344no—
495C22—344no—
496C22—344no—
497C22—684no—
498C22—682no—
499C22—682no—
500C22—682no—
501C22—682no—
502C22—684no—
503C22#1176374511yescharacteristic
504C22C4×C22⋊#59511yescharacteristic
505C22C4×C4⋊#59511yescharacteristic
506C22#1176375111yescharacteristic
507C22#1176375211yescharacteristic
508C22#1176375311yescharacteristic
509C22#1176375411yescharacteristic
510C22C2×#1058755111yescharacteristic
511C22C2×#1058753911yescharacteristic
512C22#1176378811yescharacteristic
513C22#1176378811yescharacteristic
514C4—22no—
515C4—22no—
516C4—42no—
517C4—42no—
518C4—682no—
519C4—682no—
520C4—682no—
521C4—1368no—
522C2—21no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—344no—
527C2—344no—
528C2#1454396011yescharacteristic
529C2C4×#1058755111yescharacteristic
530C2C4×#1058753911yescharacteristic
531C2#1454464411yescharacteristic
532C2#1454464511yescharacteristic
533C2#1454467911yescharacteristic
534C2#1454468111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC22×C42×C17C4
socleC23×C17C2×C22⋊C4
prime radical, cosocleC24×D17C23
hypercenterC22×C42#595
hypocenterC17#10801
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
9. #11763687C4semidirect
13. C22×C4×Dic17C4semidirect
16. C2×#10587502C4semidirect
17. C2×#10587502C4semidirect
18. C22×C42×C17C4semidirect
264. C22×C42#595semidirect
323. C17#10801semidirect

Maximal subgroups

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

subgroupindex
C2×#117636872
#145439582
C2×C4×#632272
#1080117