Finite Group Databasebeta

← #17950968

Subgroups — #17950968

Order 4352.

1026 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545228C211yesmaximal, characteristic
2C2×#11763751C211yesmaximal, characteristic
3#14543647C214yesmaximal, complemented
4C2×#11762772C211yesmaximal, characteristic
5C2×#10587677—21no—
6C22×C4⋊#595—21no—
7C22×C22⋊#595—21no—
8#11763752C412yescomplemented
9#11763751—21no—
10#11763751—21no—
11#11763751—21no—
12#11763751C412yescomplemented
13#11763751C2212yes—
14#11763751C2212yes—
15#11763750—21no—
16C4×C22⋊#595—21no—
17C4×C22⋊#595C412yescomplemented
18C2×(C2×#595)⋊C4C412yescomplemented
19C23×C4×D17C2211yescharacteristic
20C22×#63223C411yescharacteristic, complemented
21#11762772—21no—
22#11762772—21no—
23#11762772—21no—
24#11762772—21no—
25C2×#10587491C412yescomplemented
26C2×#10587491C2212yes—
27C22×M16×C17C411yescharacteristic, complemented
28C24×D17D411yescharacteristic
29C23×#595—22no—
30C23×C4×C17C2×C411yescharacteristic
31C23×Dic17Q811yescharacteristic
32C22×C4×D17—42no—
33C22×C4×D17—42no—
34C22×C4×D17C2×C411yescharacteristic
35C22×C4×D17C2×C411yescharacteristic
36C22×C4×D17C2×C411yescharacteristic
37C22×C4×D17C2×C411yescharacteristic
38C22×C4×D17C2×C411yescharacteristic
39C22×C4×D17D411yescharacteristic
40C22×C4×D17D411yescharacteristic
41C22×C4×D17D411yescharacteristic
42C22×C4×D17D411yescharacteristic
43C22×C4×D17D411yescharacteristic
44C22×C4×D17Q811yescharacteristic
45C22×C4×D17C2311yescharacteristic
46C2×C22⋊#595—22no—
47C2×C22⋊#595—22no—
48C2×C22⋊#595—22no—
49C2×C22⋊#595—22no—
50C2×C22⋊#595—22no—
51C2×C22⋊#595—44no—
52#10587677—42no—
53#10587677—42no—
54C2×C4⋊#595—22no—
55C2×C4⋊#595—22no—
56C2×C4⋊#595—22no—
57C2×C4⋊#595—42no—
58C2×C4⋊#595—42no—
59C2×C4×#595—22no—
60C2×M16×C17—21no—
61C2×M16×C17—21no—
62C2×M16×C17—42no—
63C22×C8×C17C2×C412yescomplemented
64C2×#63223—21no—
65C2×#63223—21no—
66C2×#63223—42no—
67C22×#3622C2×C412yescomplemented
68(C2×#595)⋊C4—22no—
69(C2×#595)⋊C4—22no—
70(C2×#595)⋊C4C2×C414yes—
71(C2×#595)⋊C4C2×C414yescomplemented
72#10587491—22no—
73#10587491—22no—
74#10587491—22no—
75#10587491—22no—
76C24×C17C4⋊C411yescharacteristic
77C23×D17—22no—
78C23×D17—22no—
79C23×D17—42no—
80C23×D17—42no—
81C23×D17C22⋊C411yescharacteristic
82C23×D17C22⋊C411yescharacteristic
83C23×D17C22⋊C411yescharacteristic
84C23×D17C22⋊C411yescharacteristic
85C23×D17C4⋊C411yescharacteristic
86C23×D17C2×D411yescharacteristic
87C22×#595—24no—
88C22×#595—24no—
89C22×#595—44no—
90C22×#595—44no—
91C22×#595—44no—
92C22×C4×C17—22no—
93C22×C4×C17—22no—
94C22×C4×C17C4211yescharacteristic
95C22×C4×C17C4211yescharacteristic
96C22×C4×C17C22⋊C411yescharacteristic
97C22×C4×C17C22⋊C411yescharacteristic
98C22×C4×C17C4⋊C411yescharacteristic
99C22×C4×C17C22×C411yescharacteristic
100C22×Dic17—42no—
101C22×Dic17C4⋊C411yescharacteristic
102C22×Dic17C4⋊C411yescharacteristic
103C22×Dic17C4⋊C411yescharacteristic
104C22×Dic17C4⋊C411yescharacteristic
105C22×Dic17C4⋊C411yescharacteristic
106C22×Dic17C2×Q811yescharacteristic
107C2×C4×D17—22no—
108C2×C4×D17—22no—
109C2×C4×D17—22no—
110C2×C4×D17—22no—
111C2×C4×D17—42no—
112C2×C4×D17—42no—
113C2×C4×D17—41no—
114C2×C4×D17—41no—
115C2×C4×D17—42no—
116C2×C4×D17—41no—
117C2×C4×D17—41no—
118C2×C4×D17—41no—
119C2×C4×D17—41no—
120C2×C4×D17—42no—
121C2×C4×D17—41no—
122C2×C4×D17—41no—
123C2×C4×D17—42no—
124C2×C4×D17—42no—
125C2×C4×D17C4211yescharacteristic
126C2×C4×D17C4211yescharacteristic
127C2×C4×D17C22⋊C411yescharacteristic
128C2×C4×D17C22⋊C411yescharacteristic
129C2×C4×D17C22⋊C411yescharacteristic
130C2×C4×D17C22⋊C411yescharacteristic
131C2×C4×D17C22⋊C411yescharacteristic
132C2×C4×D17C22⋊C411yescharacteristic
133C2×C4×D17C4⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C4⋊C411yescharacteristic
136C2×C4×D17C4⋊C411yescharacteristic
137C2×C4×D17C22×C411yescharacteristic
138C2×C4×D17C22×C411yescharacteristic
139C2×C4×D17C2×D411yescharacteristic
140C2×C4×D17C2×D411yescharacteristic
141C22⋊#595—44no—
142C22⋊#595—44no—
143C22⋊#595—44no—
144C22⋊#595—42no—
145C22⋊#595—44no—
146C22⋊#595—42no—
147C4⋊#595—44no—
148C4⋊#595—42no—
149C4⋊#595—42no—
150C4⋊#595—42no—
151C4⋊#595—42no—
152C4×#595—44no—
153M16×C17—42no—
154M16×C17—42no—
155C2×C8×C17—22no—
156C2×C8×C17—42no—
157#63223—42no—
158#63223—42no—
159C2×#3622—22no—
160C2×#3622—42no—
161#7983—171nomaximal, Sylow
162C23×C17—22no—
163C23×C17—22no—
164C23×C17—41no—
165C23×C17#9511yescharacteristic
166C23×C17#9511yescharacteristic
167C23×C17C2×C4⋊C411yescharacteristic
168C22×D17—22no—
169C22×D17—22no—
170C22×D17—21no—
171C22×D17—21no—
172C22×D17—22no—
173C22×D17—22no—
174C22×D17—22no—
175C22×D17—22no—
176C22×D17—22no—
177C22×D17—22no—
178C22×D17—21no—
179C22×D17—21no—
180C22×D17—41no—
181C22×D17—41no—
182C22×D17—41no—
183C22×D17—41no—
184C22×D17—41no—
185C22×D17—41no—
186C22×D17—41no—
187C22×D17—48no—
188C22×D17—48no—
189C22×D17#9511yescharacteristic
190C22×D17#9511yescharacteristic
191C22×D17C2×C22⋊C411yescharacteristic
192C22×D17C2×C22⋊C411yescharacteristic
193C22×D17AGL(1,ℤ/8)12yes—
194C22×D17#13712yes—
195C2×#595—44no—
196C2×#595—44no—
197C2×#595—44no—
198C2×#595—44no—
199C2×#595—44no—
200C2×#595—44no—
201C2×#595—88no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—21no—
206C2×C4×C17—21no—
207C2×C4×C17—21no—
208C2×C4×C17—21no—
209C2×C4×C17#9511yescharacteristic
210C2×C4×C17#9511yescharacteristic
211C2×C4×C17#9912yes—
212C2×C4×C17#9912yes—
213C2×C4×C17C2×C4211yescharacteristic
214C2×C4×C17C2×C22⋊C411yescharacteristic
215C2×Dic17—22no—
216C2×Dic17—22no—
217C2×Dic17—41no—
218C2×Dic17—41no—
219C2×Dic17—41no—
220C2×Dic17—41no—
221C2×Dic17#9511yescharacteristic
222C2×Dic17#9511yescharacteristic
223C2×Dic17C2×C4⋊C411yescharacteristic
224C2×Dic17C2×C4⋊C411yescharacteristic
225C4×D17—22no—
226C4×D17—22no—
227C4×D17—22no—
228C4×D17—22no—
229C4×D17—21no—
230C4×D17—21no—
231C4×D17—21no—
232C4×D17—21no—
233C4×D17—21no—
234C4×D17—21no—
235C4×D17—21no—
236C4×D17—21no—
237C4×D17—41no—
238C4×D17—41no—
239C4×D17—41no—
240C4×D17—41no—
241C4×D17—41no—
242C4×D17—41no—
243C4×D17—41no—
244C4×D17—41no—
245C8×C17—42no—
246#3622—42no—
247C2×#407—171no—
248#2280—171no—
249C2×#380—171no—
250#1289—174no—
251C22×C17—21no—
252C22×C17—21no—
253C22×C17—21no—
254C22×C17—21no—
255C22×C17—21no—
256C22×C17—21no—
257C22×C17—21no—
258C22×C17—44no—
259C22×C17#34212yes—
260C22×C17C2×#9511yescharacteristic
261C22×C17#42812yes—
262C2×D17—24no—
263C2×D17—24no—
264C2×D17—21no—
265C2×D17—21no—
266C2×D17—21no—
267C2×D17—21no—
268C2×D17—21no—
269C2×D17—21no—
270C2×D17—21no—
271C2×D17—21no—
272C2×D17—21no—
273C2×D17—42no—
274C2×D17—42no—
275C2×D17—44no—
276C2×D17—44no—
277C2×D17—44no—
278C2×D17—42no—
279C2×D17—42no—
280C2×D17H(3,ℤ/4)12yes—
281C2×D17#41712yes—
282C2×D17#41811yescharacteristic
283C2×D17#41911yescharacteristic
284#595—84no—
285#595—84no—
286C4×C17—21no—
287C4×C17—21no—
288C4×C17#34212yes—
289C4×C17C2×#9911yescharacteristic
290C4×C17C2×#9911yescharacteristic
291Dic17—21no—
292Dic17—21no—
293Dic17—21no—
294Dic17—21no—
295C24×C4—171no—
296C22×M16—171no—
297C22×M16#59511yescharacteristic, complemented
298C2×#117—341no—
299C22×C4⋊C4—341no—
300C22×C22⋊C4—341no—
301#407—341no—
302#407—341no—
303#407—341no—
304#407—341no—
305C2×C22⋊C8—172no—
306C2×C22⋊C8—172no—
307#381—172no—
308#380—172no—
309#380—172no—
310#380—172no—
311#380—341no—
312#380—341no—
313#380—341no—
314#379—341no—
315C4×C22⋊C4—172no—
316C4×C22⋊C4—341no—
317C2×#95—172no—
318C2×C17—22no—
319C2×C17—22no—
320C2×C17—41no—
321C2×C17C2×H(3,ℤ/4)11yescharacteristic
322C2×C17#173611yescharacteristic
323C2×C17C2×#34211yescharacteristic
324D17—21no—
325D17—22no—
326D17—22no—
327D17—21no—
328D17—41no—
329C25—171no—
330C23×C4—171no—
331C23×C4—171no—
332C23×C4—171no—
333C23×C4—171no—
334C23×C4—171no—
335C23×C4—171no—
336C23×C4—171no—
337C23×C4—171no—
338C23×C4—171no—
339C23×C4—171no—
340C23×C4—171no—
341C23×C4—171no—
342C23×C4—171no—
343C23×C4—342no—
344C23×C4—682no—
345C23×C4—682no—
346C23×C4C2×#59511yescharacteristic
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—42no—
350C2×M16—341no—
351C2×M16—341no—
352C2×M16—682no—
353C22×C8—172no—
354C22×C8C2×#59512yescomplemented
355#117—682no—
356#117—682no—
357C2×C4⋊C4—342no—
358C2×C4⋊C4—342no—
359C2×C4⋊C4—342no—
360C2×C4⋊C4—682no—
361C2×C4⋊C4—682no—
362C2×C22⋊C4—342no—
363C2×C22⋊C4—342no—
364C2×C22⋊C4—342no—
365C2×C22⋊C4—342no—
366C2×C22⋊C4—342no—
367C2×C22⋊C4—684no—
368C2×C42—342no—
369C22⋊C8—342no—
370C22⋊C8—342no—
371C22⋊C8—342no—
372C22⋊C8—342no—
373#95—174no—
374#95—174no—
375#95—342no—
376#95—342no—
377C17#798311yescharacteristic, complemented, Sylow
378C24—171no—
379C24—171no—
380C24—171no—
381C24—171no—
382C24—171no—
383C24—171no—
384C24—342no—
385C24—342no—
386C24—682no—
387C24—682no—
388C24C4⋊#59511yescharacteristic
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—171no—
392C22×C4—171no—
393C22×C4—171no—
394C22×C4—171no—
395C22×C4—171no—
396C22×C4—171no—
397C22×C4—171no—
398C22×C4—171no—
399C22×C4—171no—
400C22×C4—171no—
401C22×C4—171no—
402C22×C4—171no—
403C22×C4—171no—
404C22×C4—171no—
405C22×C4—171no—
406C22×C4—171no—
407C22×C4—171no—
408C22×C4—171no—
409C22×C4—171no—
410C22×C4—171no—
411C22×C4—171no—
412C22×C4—171no—
413C22×C4—342no—
414C22×C4—342no—
415C22×C4—342no—
416C22×C4—342no—
417C22×C4—344no—
418C22×C4—344no—
419C22×C4—681no—
420C22×C4—681no—
421C22×C4—681no—
422C22×C4—681no—
423C22×C4—681no—
424C22×C4—681no—
425C22×C4—681no—
426C22×C4—681no—
427C22×C4—682no—
428C22×C4—682no—
429C22×C4—682no—
430C22×C4—682no—
431C22×C4—682no—
432C22×C4—682no—
433C22×C4—682no—
434C22×C4—684no—
435C22×C4—684no—
436C22×C4—684no—
437C22×C4C4×#59511yescharacteristic
438C22×C4C4×#59511yescharacteristic
439C22×C4C4⋊#59511yescharacteristic
440C22×C4C22⋊#59511yescharacteristic
441C22×C4C22⋊#59511yescharacteristic
442C22×C4C22×#59511yescharacteristic
443M16—42no—
444M16—42no—
445M16—682no—
446M16—682no—
447C2×C8—22no—
448C2×C8—42no—
449C2×C8—342no—
450C2×C8—682no—
451C4⋊C4—682no—
452C4⋊C4—682no—
453C4⋊C4—684no—
454C4⋊C4—682no—
455C4⋊C4—682no—
456C22⋊C4—682no—
457C22⋊C4—682no—
458C22⋊C4—684no—
459C22⋊C4—684no—
460C22⋊C4—684no—
461C22⋊C4—684no—
462C42—684no—
463C23—22no—
464C23—22no—
465C23—41no—
466C23—171no—
467C23—171no—
468C23—171no—
469C23—172no—
470C23—172no—
471C23—171no—
472C23—341no—
473C23—342no—
474C23—341no—
475C23—341no—
476C23—342no—
477C23—342no—
478C23—342no—
479C23—341no—
480C23—342no—
481C23—342no—
482C23—342no—
483C23—342no—
484C23—681no—
485C23—681no—
486C23—681no—
487C23—681no—
488C23—681no—
489C23—681no—
490C23—681no—
491C23—688no—
492C23—688no—
493C23(C2×#595)⋊C411yescharacteristic
494C23(C2×#595)⋊C411yescharacteristic
495C23C2×C4⋊#59511yescharacteristic
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—171no—
504C2×C4—171no—
505C2×C4—171no—
506C2×C4—171no—
507C2×C4—342no—
508C2×C4—342no—
509C2×C4—341no—
510C2×C4—341no—
511C2×C4—341no—
512C2×C4—341no—
513C2×C4—341no—
514C2×C4—341no—
515C2×C4—341no—
516C2×C4—341no—
517C2×C4—342no—
518C2×C4—342no—
519C2×C4—342no—
520C2×C4—342no—
521C2×C4—681no—
522C2×C4—681no—
523C2×C4—681no—
524C2×C4—681no—
525C2×C4—681no—
526C2×C4—681no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4—681no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—681no—
533C2×C4—684no—
534C2×C4—684no—
535C2×C4—684no—
536C2×C4—684no—
537C2×C4—684no—
538C2×C4—684no—
539C2×C4—1368no—
540C2×C4#1058753912yes—
541C2×C4(C2×#595)⋊C411yescharacteristic
542C2×C4(C2×#595)⋊C411yescharacteristic
543C2×C4#1058755112yes—
544C2×C4C2×C4×#59511yescharacteristic
545C2×C4C2×C22⋊#59511yescharacteristic
546C8—42no—
547C8—682no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—44no—
556C22—172no—
557C22—171no—
558C22—172no—
559C22—171no—
560C22—344no—
561C22—344no—
562C22—341no—
563C22—341no—
564C22—341no—
565C22—341no—
566C22—341no—
567C22—341no—
568C22—341no—
569C22—341no—
570C22—341no—
571C22—682no—
572C22—682no—
573C22—684no—
574C22—684no—
575C22—684no—
576C22—682no—
577C22—682no—
578C22#1176368712yes—
579C22C2×(C2×#595)⋊C411yescharacteristic
580C22#1176382012yes—
581C4—21no—
582C4—21no—
583C4—341no—
584C4—341no—
585C4—341no—
586C4—341no—
587C4—1364no—
588C4—1364no—
589C4#1176368712yes—
590C4C2×#1058755111yescharacteristic
591C4C2×#1058753911yescharacteristic
592C2—22no—
593C2—22no—
594C2—41no—
595C2—341no—
596C2—342no—
597C2—342no—
598C2—341no—
599C2—681no—
600C2#1454445611yescharacteristic
601C2#1454447211yescharacteristic
602C2C2×#1176368711yescharacteristic
subgroupG/H
centerC22C2×(C2×#595)⋊C4
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC22×M16×C17C4
socleC22×C17C2×#95
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC22×M16#595
hypocenterC17#7983
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #14543647C2semidirect
8. #11763752C4semidirect
12. #11763751C4semidirect
17. C4×C22⋊#595C4semidirect
18. C2×(C2×#595)⋊C4C4semidirect
20. C22×#63223C4semidirect
25. C2×#10587491C4semidirect
27. C22×M16×C17C4semidirect
63. C22×C8×C17C2×C4semidirect
67. C22×#3622C2×C4semidirect
71. (C2×#595)⋊C4C2×C4semidirect
297. C22×M16#595semidirect
354. C22×C8C2×#595semidirect
377. C17#7983semidirect

Maximal subgroups

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

subgroupindex
#145452282
C2×#117637512
#145436472
C2×#117627722
#798317