Finite Group Databasebeta

← #17951261

Subgroups — #17951261

Order 4352.

1090 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545228C211yesmaximal, characteristic
2C2×C4×C22⋊#595C211yesmaximal, characteristic
3#14543664C214yesmaximal, complemented
4C2×#11762772C211yesmaximal, characteristic
5C2×#10587677—21no—
6C22×C22⋊#595—21no—
7C22×C4×#595—21no—
8#11763752C412yescomplemented
9#11763751—21no—
10#11763751C412yescomplemented
11#11763750—21no—
12C4×C22⋊#595—21no—
13C4×C22⋊#595—21no—
14C4×C22⋊#595—21no—
15C4×C22⋊#595C412yescomplemented
16C4×C22⋊#595C2212yes—
17C4×C22⋊#595C2212yes—
18C2×(C2×#595)⋊C4C412yescomplemented
19C23×C4×D17C2211yescharacteristic
20C22×#63223C411yescharacteristic, complemented
21#11762772—21no—
22#11762772—21no—
23#11762772C412yescomplemented
24#11762772C2212yes—
25C2×#10587491—21no—
26C2×#10587491—21no—
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—28no—
47C2×C22⋊#595—22no—
48C2×C22⋊#595—22no—
49C2×C22⋊#595—22no—
50C2×C22⋊#595—22no—
51C2×C22⋊#595—22no—
52#10587677—42no—
53#10587677—42no—
54C2×C4⋊#595—22no—
55C2×C4×#595—22no—
56C2×C4×#595—22no—
57C2×C4×#595—22no—
58C2×C4×#595—42no—
59C2×C4×#595—42no—
60C2×M16×C17—21no—
61C2×M16×C17—42no—
62C2×M16×C17C2×C412yescomplemented
63C22×C8×C17—21no—
64C2×#63223—21no—
65C2×#63223—42no—
66C2×#63223C2×C412yescomplemented
67C22×#3622—21no—
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—24no—
78C23×D17—42no—
79C23×D17—42no—
80C23×D17C22⋊C411yescharacteristic
81C23×D17C22⋊C411yescharacteristic
82C23×D17C22⋊C411yescharacteristic
83C23×D17C22⋊C411yescharacteristic
84C23×D17C4⋊C411yescharacteristic
85C23×D17C2×D411yescharacteristic
86C22×#595—28no—
87C22×#595—24no—
88C22×#595—24no—
89C22×#595—44no—
90C22×#595—44no—
91C22×C4×C17—22no—
92C22×C4×C17—22no—
93C22×C4×C17C4211yescharacteristic
94C22×C4×C17C4211yescharacteristic
95C22×C4×C17C22⋊C411yescharacteristic
96C22×C4×C17C22⋊C411yescharacteristic
97C22×C4×C17C4⋊C411yescharacteristic
98C22×C4×C17C22×C411yescharacteristic
99C22×Dic17—42no—
100C22×Dic17C4⋊C411yescharacteristic
101C22×Dic17C4⋊C411yescharacteristic
102C22×Dic17C4⋊C411yescharacteristic
103C22×Dic17C4⋊C411yescharacteristic
104C22×Dic17C4⋊C411yescharacteristic
105C22×Dic17C2×Q811yescharacteristic
106C2×C4×D17—22no—
107C2×C4×D17—22no—
108C2×C4×D17—22no—
109C2×C4×D17—22no—
110C2×C4×D17—42no—
111C2×C4×D17—42no—
112C2×C4×D17—41no—
113C2×C4×D17—41no—
114C2×C4×D17—42no—
115C2×C4×D17—41no—
116C2×C4×D17—41no—
117C2×C4×D17—41no—
118C2×C4×D17—41no—
119C2×C4×D17—42no—
120C2×C4×D17—41no—
121C2×C4×D17—41no—
122C2×C4×D17—42no—
123C2×C4×D17—42no—
124C2×C4×D17C4211yescharacteristic
125C2×C4×D17C4211yescharacteristic
126C2×C4×D17C22⋊C411yescharacteristic
127C2×C4×D17C22⋊C411yescharacteristic
128C2×C4×D17C22⋊C411yescharacteristic
129C2×C4×D17C22⋊C411yescharacteristic
130C2×C4×D17C22⋊C411yescharacteristic
131C2×C4×D17C22⋊C411yescharacteristic
132C2×C4×D17C4⋊C411yescharacteristic
133C2×C4×D17C4⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C4⋊C411yescharacteristic
136C2×C4×D17C22×C411yescharacteristic
137C2×C4×D17C22×C411yescharacteristic
138C2×C4×D17C2×D411yescharacteristic
139C2×C4×D17C2×D411yescharacteristic
140C22⋊#595—28no—
141C22⋊#595—28no—
142C22⋊#595—44no—
143C22⋊#595—44no—
144C22⋊#595—44no—
145C4⋊#595—44no—
146C4×#595—44no—
147C4×#595—42no—
148C4×#595—42no—
149C4×#595—42no—
150C4×#595—42no—
151M16×C17—42no—
152M16×C17—42no—
153C2×C8×C17—22no—
154C2×C8×C17—42no—
155#63223—42no—
156#63223—42no—
157C2×#3622—22no—
158C2×#3622—42no—
159#8051—171nomaximal, Sylow
160C23×C17—22no—
161C23×C17—22no—
162C23×C17—41no—
163C23×C17#9511yescharacteristic
164C23×C17#9511yescharacteristic
165C23×C17C2×C4⋊C411yescharacteristic
166C22×D17—22no—
167C22×D17—22no—
168C22×D17—22no—
169C22×D17—22no—
170C22×D17—22no—
171C22×D17—22no—
172C22×D17—22no—
173C22×D17—22no—
174C22×D17—22no—
175C22×D17—22no—
176C22×D17—41no—
177C22×D17—41no—
178C22×D17—41no—
179C22×D17—41no—
180C22×D17—41no—
181C22×D17—41no—
182C22×D17—41no—
183C22×D17—416no—
184C22×D17#9511yescharacteristic
185C22×D17#9511yescharacteristic
186C22×D17#10414yes—
187C22×D17C2×C22⋊C411yescharacteristic
188C22×D17C2×C22⋊C411yescharacteristic
189C2×#595—28no—
190C2×#595—44no—
191C2×#595—416no—
192C2×#595—44no—
193C2×#595—44no—
194C2×#595—44no—
195C2×#595—44no—
196C2×C4×C17—22no—
197C2×C4×C17—22no—
198C2×C4×C17—22no—
199C2×C4×C17—21no—
200C2×C4×C17—21no—
201C2×C4×C17—21no—
202C2×C4×C17—21no—
203C2×C4×C17#9511yescharacteristic
204C2×C4×C17#9511yescharacteristic
205C2×C4×C17#9912yes—
206C2×C4×C17#9912yes—
207C2×C4×C17C2×C4211yescharacteristic
208C2×C4×C17C2×C22⋊C411yescharacteristic
209C2×Dic17—22no—
210C2×Dic17—22no—
211C2×Dic17—41no—
212C2×Dic17—41no—
213C2×Dic17—41no—
214C2×Dic17—41no—
215C2×Dic17#9511yescharacteristic
216C2×Dic17#9511yescharacteristic
217C2×Dic17C2×C4⋊C411yescharacteristic
218C2×Dic17C2×C4⋊C411yescharacteristic
219C4×D17—22no—
220C4×D17—22no—
221C4×D17—22no—
222C4×D17—22no—
223C4×D17—21no—
224C4×D17—21no—
225C4×D17—21no—
226C4×D17—21no—
227C4×D17—21no—
228C4×D17—21no—
229C4×D17—21no—
230C4×D17—21no—
231C4×D17—41no—
232C4×D17—41no—
233C4×D17—41no—
234C4×D17—41no—
235C4×D17—41no—
236C4×D17—41no—
237C4×D17—41no—
238C4×D17—41no—
239C8×C17—42no—
240#3622—42no—
241C2×#407—171no—
242#2280—171no—
243C2×C4×C22⋊C4—171no—
244#1297—174no—
245C22×C17—21no—
246C22×C17—21no—
247C22×C17—21no—
248C22×C17—21no—
249C22×C17—21no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—44no—
253C22×C17#33912yes—
254C22×C17#34212yes—
255C22×C17C2×#9511yescharacteristic
256C2×D17—28no—
257C2×D17—21no—
258C2×D17—21no—
259C2×D17—21no—
260C2×D17—21no—
261C2×D17—21no—
262C2×D17—21no—
263C2×D17—21no—
264C2×D17—21no—
265C2×D17—21no—
266C2×D17—44no—
267C2×D17—44no—
268C2×D17—44no—
269C2×D17—44no—
270C2×D17—44no—
271C2×D17#33912yes—
272C2×D17C2×#10412yes—
273C2×D17#42112yes—
274#595—48no—
275#595—84no—
276C4×C17—21no—
277C4×C17—21no—
278C4×C17#34212yes—
279C4×C17C2×#9911yescharacteristic
280C4×C17C2×#9911yescharacteristic
281Dic17—21no—
282Dic17—21no—
283Dic17—21no—
284Dic17—21no—
285C24×C4—171no—
286C22×M16—171no—
287C22×M16#59511yescharacteristic, complemented
288C2×#117—341no—
289C22×C22⋊C4—341no—
290C22×C42—341no—
291#407—172no—
292#407—172no—
293#407—341no—
294#407—341no—
295C2×C22⋊C8—341no—
296C2×C22⋊C8—341no—
297#381—172no—
298#380—172no—
299#380—341no—
300#379—341no—
301C4×C22⋊C4—172no—
302C4×C22⋊C4—172no—
303C4×C22⋊C4—172no—
304C4×C22⋊C4—341no—
305C4×C22⋊C4—341no—
306C4×C22⋊C4—341no—
307C2×#95—172no—
308C2×C17—22no—
309C2×C17—22no—
310C2×C17—41no—
311C2×C17C2×#33911yescharacteristic
312C2×C17#173311yescharacteristic
313C2×C17C2×#34211yescharacteristic
314D17—22no—
315D17—22no—
316D17—22no—
317D17—41no—
318C25—171no—
319C23×C4—171no—
320C23×C4—171no—
321C23×C4—171no—
322C23×C4—171no—
323C23×C4—171no—
324C23×C4—171no—
325C23×C4—171no—
326C23×C4—171no—
327C23×C4—171no—
328C23×C4—171no—
329C23×C4—171no—
330C23×C4—171no—
331C23×C4—171no—
332C23×C4—342no—
333C23×C4—682no—
334C23×C4—682no—
335C23×C4C2×#59511yescharacteristic
336C2×M16—21no—
337C2×M16—42no—
338C2×M16—172no—
339C2×M16—341no—
340C2×M16—682no—
341C2×M16C2×#59512yescomplemented
342C22×C8—21no—
343C22×C8—341no—
344#117—682no—
345#117—682no—
346C2×C4⋊C4—342no—
347C2×C22⋊C4—342no—
348C2×C22⋊C4—342no—
349C2×C22⋊C4—348no—
350C2×C22⋊C4—342no—
351C2×C22⋊C4—342no—
352C2×C22⋊C4—342no—
353C2×C42—342no—
354C2×C42—342no—
355C2×C42—342no—
356C2×C42—682no—
357C2×C42—682no—
358C22⋊C8—342no—
359C22⋊C8—342no—
360C22⋊C8—342no—
361C22⋊C8—342no—
362#95—174no—
363#95—174no—
364#95—342no—
365#95—342no—
366C17#805111yescharacteristic, complemented, Sylow
367C24—171no—
368C24—171no—
369C24—171no—
370C24—171no—
371C24—171no—
372C24—171no—
373C24—344no—
374C24—682no—
375C24—682no—
376C24C4⋊#59511yescharacteristic
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—171no—
380C22×C4—171no—
381C22×C4—171no—
382C22×C4—171no—
383C22×C4—171no—
384C22×C4—171no—
385C22×C4—171no—
386C22×C4—171no—
387C22×C4—171no—
388C22×C4—171no—
389C22×C4—171no—
390C22×C4—171no—
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—342no—
402C22×C4—342no—
403C22×C4—342no—
404C22×C4—342no—
405C22×C4—344no—
406C22×C4—348no—
407C22×C4—344no—
408C22×C4—681no—
409C22×C4—681no—
410C22×C4—681no—
411C22×C4—681no—
412C22×C4—681no—
413C22×C4—681no—
414C22×C4—681no—
415C22×C4—681no—
416C22×C4—682no—
417C22×C4—682no—
418C22×C4—682no—
419C22×C4—682no—
420C22×C4—682no—
421C22×C4—682no—
422C22×C4—682no—
423C22×C4—684no—
424C22×C4—684no—
425C22×C4C4×#59511yescharacteristic
426C22×C4C4×#59511yescharacteristic
427C22×C4C4⋊#59511yescharacteristic
428C22×C4C22⋊#59511yescharacteristic
429C22×C4C22⋊#59511yescharacteristic
430C22×C4C22×#59511yescharacteristic
431M16—42no—
432M16—42no—
433M16—682no—
434M16—682no—
435C2×C8—22no—
436C2×C8—42no—
437C2×C8—342no—
438C2×C8—682no—
439C4⋊C4—684no—
440C22⋊C4—348no—
441C22⋊C4—348no—
442C22⋊C4—684no—
443C22⋊C4—684no—
444C22⋊C4—684no—
445C42—682no—
446C42—682no—
447C42—684no—
448C42—682no—
449C42—682no—
450C23—22no—
451C23—22no—
452C23—41no—
453C23—171no—
454C23—171no—
455C23—171no—
456C23—174no—
457C23—171no—
458C23—342no—
459C23—342no—
460C23—342no—
461C23—342no—
462C23—342no—
463C23—342no—
464C23—342no—
465C23—342no—
466C23—342no—
467C23—342no—
468C23—681no—
469C23—681no—
470C23—681no—
471C23—681no—
472C23—681no—
473C23—681no—
474C23—681no—
475C23—6816no—
476C23(C2×#595)⋊C411yescharacteristic
477C23(C2×#595)⋊C411yescharacteristic
478C23C2×C4⋊#59511yescharacteristic
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—171no—
487C2×C4—171no—
488C2×C4—171no—
489C2×C4—171no—
490C2×C4—342no—
491C2×C4—342no—
492C2×C4—341no—
493C2×C4—341no—
494C2×C4—341no—
495C2×C4—341no—
496C2×C4—341no—
497C2×C4—341no—
498C2×C4—341no—
499C2×C4—341no—
500C2×C4—342no—
501C2×C4—342no—
502C2×C4—342no—
503C2×C4—342no—
504C2×C4—348no—
505C2×C4—681no—
506C2×C4—681no—
507C2×C4—681no—
508C2×C4—681no—
509C2×C4—681no—
510C2×C4—681no—
511C2×C4—681no—
512C2×C4—681no—
513C2×C4—681no—
514C2×C4—681no—
515C2×C4—681no—
516C2×C4—681no—
517C2×C4—684no—
518C2×C4—684no—
519C2×C4—6816no—
520C2×C4—684no—
521C2×C4—684no—
522C2×C4—684no—
523C2×C4#1058753912yes—
524C2×C4(C2×#595)⋊C411yescharacteristic
525C2×C4(C2×#595)⋊C411yescharacteristic
526C2×C4#1058755112yes—
527C2×C4C2×C4×#59511yescharacteristic
528C2×C4C2×C22⋊#59511yescharacteristic
529C8—42no—
530C8—682no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—44no—
539C22—172no—
540C22—172no—
541C22—172no—
542C22—348no—
543C22—341no—
544C22—341no—
545C22—341no—
546C22—341no—
547C22—341no—
548C22—341no—
549C22—341no—
550C22—341no—
551C22—341no—
552C22—684no—
553C22—684no—
554C22—684no—
555C22—684no—
556C22—684no—
557C22#1176368112yes—
558C22#1176368712yes—
559C22C2×(C2×#595)⋊C411yescharacteristic
560C4—21no—
561C4—21no—
562C4—341no—
563C4—341no—
564C4—341no—
565C4—341no—
566C4—688no—
567C4—1364no—
568C4#1176368712yes—
569C4C2×#1058755111yescharacteristic
570C4C2×#1058753911yescharacteristic
571C2—22no—
572C2—22no—
573C2—41no—
574C2—342no—
575C2—342no—
576C2—342no—
577C2—681no—
578C2C2×#1176368111yescharacteristic
579C2#1454446611yescharacteristic
580C2C2×#1176368711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC22×M16×C17C4
socleC22×C17C2×#95
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC22×M16#595
hypocenterC17#8051
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #14543664C2semidirect
8. #11763752C4semidirect
10. #11763751C4semidirect
15. C4×C22⋊#595C4semidirect
18. C2×(C2×#595)⋊C4C4semidirect
20. C22×#63223C4semidirect
23. #11762772C4semidirect
27. C22×M16×C17C4semidirect
62. C2×M16×C17C2×C4semidirect
66. C2×#63223C2×C4semidirect
71. (C2×#595)⋊C4C2×C4semidirect
287. C22×M16#595semidirect
341. C2×M16C2×#595semidirect
366. C17#8051semidirect

Maximal subgroups

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

subgroupindex
#145452282
C2×C4×C22⋊#5952
#145436642
C2×#117627722
#805117