Finite Group Databasebeta

← #17969480

Subgroups — #17969480

Order 4352.

1866 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545228C212yesmaximal, complemented
2#14544679C212yesmaximal, complemented
3#14544644C214yesmaximal, complemented
4#14544610C212yesmaximal
5C4×#10587551C214yesmaximal, complemented
6C22×C4×C22⋊D17C211yesmaximal, characteristic
7C2×#10587677—22no—
8C2×#10587551C2218yes—
9#11763752—22no—
10#11763751—22no—
11#11763751C2214yescomplemented
12#11763750C2214yes—
13C4×C22⋊#595—22no—
14C4×C22⋊#595C2214yescomplemented
15#11763687C2218yescomplemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C2×C4×C22⋊D17—22no—
19C2×C4×C22⋊D17—22no—
20C2×C4×C22⋊D17—22no—
21C2×C4×C22⋊D17—22no—
22C2×C4×C22⋊D17C412yescomplemented
23C2×C4×C22⋊D17C412yescomplemented
24C2×C4×C22⋊D17C2212yes—
25C2×C4×C22⋊D17C2212yes—
26C22×#63225C411yescharacteristic, complemented
27C22×C22⋊Dic17C411yescharacteristic, complemented
28C22×#63227C2211yescharacteristic
29C22×C4×Dic17C411yescharacteristic, complemented
30C24×C4×C17C411yescharacteristic, complemented
31C25×C17C2×C411yescharacteristic
32C24×D17C2311yescharacteristic
33C23×C4×C17—21no—
34C23×C4×C17—21no—
35C23×C4×C17—21no—
36C23×C4×C17—21no—
37C23×C4×C17—44no—
38C23×C4×C17C2×C411yescharacteristic
39C23×C4×C17C2×C411yescharacteristic
40C23×C4×C17C2×C412yes—
41C23×C4×C17C2×C412yes—
42C22×C22⋊D17—22no—
43C22×C22⋊D17—22no—
44C22×C22⋊D17—28no—
45C22×C22⋊D17C2×C412yes—
46C22×C22⋊D17C2312yes—
47C23×Dic17C2×C411yescharacteristic
48C23×Dic17C2×C411yescharacteristic
49C23×Dic17C2×C411yescharacteristic
50C22×C4×D17—44no—
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17D412yes—
54C22×C4×D17D412yes—
55C22×C4×D17D412yes—
56C22×C4×D17D412yes—
57C22×C4×D17C2311yescharacteristic
58C22×C4×D17C2311yescharacteristic
59C2×C22⋊#595—24no—
60C2×C22⋊#595—24no—
61C2×C22⋊#595C2318yes—
62#10587677—48no—
63C2×C4⋊#595—24no—
64C2×C4×#595—24no—
65C2×C22⋊Dic17—22no—
66C2×C22⋊Dic17—22no—
67C2×C22⋊Dic17C2×C412yes—
68C2×C22⋊Dic17C2×C412yes—
69C4×C22⋊D17—24no—
70C4×C22⋊D17—24no—
71C4×C22⋊D17—24no—
72C4×C22⋊D17—24no—
73C4×C22⋊D17—24no—
74C4×C22⋊D17—24no—
75C4×C22⋊D17—24no—
76C4×C22⋊D17—24no—
77C2×#63227—22no—
78C2×#63227—22no—
79C2×#63227C2×C412yes—
80C2×#63227C2312yes—
81C2×#63225—22no—
82C2×#63225—22no—
83C2×#63225C2×C412yes—
84C2×#63225C2×C412yes—
85C2×C4×Dic17—21no—
86C2×C4×Dic17—21no—
87C2×C4×Dic17—21no—
88C2×C4×Dic17—21no—
89C2×C4×Dic17C2×C412yes—
90C2×C4×Dic17C2×C412yes—
91#10587551—216no—
92(C2×#595)⋊C4—24no—
93(C2×#595)⋊C4—24no—
94C24×C17—21no—
95C24×C17—21no—
96C24×C17—24no—
97C24×C17—42no—
98C24×C17—42no—
99C24×C17C22×C411yescharacteristic
100C24×C17C22×C412yes—
101C23×D17—24no—
102C23×D17—42no—
103C23×D17—42no—
104C23×D17C22×C411yescharacteristic
105C23×D17C2×D412yes—
106C23×D17C2×D412yes—
107C23×D17C2411yescharacteristic
108C22×#595—28no—
109C22×C4×C17—24no—
110C22×C4×C17—21no—
111C22×C4×C17—21no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—44no—
117C22×C4×C17—44no—
118C22×C4×C17—44no—
119C22×C4×C17—44no—
120C22×C4×C17—44no—
121C22×C4×C17—44no—
122C22×C4×C17—42no—
123C22×C4×C17C22⋊C411yescharacteristic
124C22×C4×C17C22⋊C411yescharacteristic
125C22×C4×C17C22⋊C411yescharacteristic
126C22×C4×C17C22⋊C411yescharacteristic
127C22×C4×C17C22×C411yescharacteristic
128C22×C4×C17C22×C411yescharacteristic
129C22×C4×C17C22×C412yes—
130C2×C22⋊D17—216no—
131C2×C22⋊D17—216no—
132C2×C22⋊D17—24no—
133C2×C22⋊D17—24no—
134C2×C22⋊D17—24no—
135C2×C22⋊D17—24no—
136C2×C22⋊D17—24no—
137C2×C22⋊D17#4118yes—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—24no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—42no—
144C22×Dic17—42no—
145C22×Dic17C22⋊C412yes—
146C22×Dic17C22⋊C412yes—
147C22×Dic17C22×C412yes—
148C22×Dic17C22×C412yes—
149C22×Dic17C22×C411yescharacteristic
150C22×Dic17C22×C411yescharacteristic
151C2×C4×D17—28no—
152C2×C4×D17—42no—
153C2×C4×D17—42no—
154C2×C4×D17—44no—
155C2×C4×D17—44no—
156C2×C4×D17—42no—
157C2×C4×D17—42no—
158C2×C4×D17—44no—
159C2×C4×D17C22⋊C412yes—
160C2×C4×D17C22⋊C412yes—
161C2×C4×D17C22⋊C412yes—
162C2×C4×D17C22⋊C412yes—
163C2×C4×D17C2×D412yes—
164C2×C4×D17C2×D412yes—
165C2×C4×D17C2×D412yes—
166C2×C4×D17C2×D412yes—
167C22⋊#595—216no—
168C22⋊#595—48no—
169C22⋊#595—48no—
170C4⋊#595—48no—
171C4×#595—48no—
172C22⋊Dic17—24no—
173C22⋊Dic17—24no—
174#63227—24no—
175#63227—24no—
176#63225—24no—
177#63225—24no—
178C4×Dic17—22no—
179C4×Dic17—22no—
180C4×Dic17—22no—
181C4×Dic17—22no—
182#20722—171nomaximal, Sylow
183C23×C17—22no—
184C23×C17—22no—
185C23×C17—22no—
186C23×C17—24no—
187C23×C17—24no—
188C23×C17—22no—
189C23×C17—22no—
190C23×C17—42no—
191C23×C17—42no—
192C23×C17—42no—
193C23×C17—416no—
194C23×C17—42no—
195C23×C17—42no—
196C23×C17—42no—
197C23×C17C2×C22⋊C411yescharacteristic
198C23×C17C2×C22⋊C411yescharacteristic
199C23×C17#11714yescomplemented
200C23×C17C23×C411yescharacteristic
201C22×D17—22no—
202C22×D17—24no—
203C22×D17—24no—
204C22×D17—24no—
205C22×D17—24no—
206C22×D17—41no—
207C22×D17—42no—
208C22×D17—41no—
209C22×D17—41no—
210C22×D17—42no—
211C22×D17—41no—
212C22×D17—416no—
213C22×D17C2×C22⋊C412yes—
214C22×D17C22×D412yes—
215C22×D17C2×#4114yes—
216C2×#595—48no—
217C2×#595—48no—
218C2×#595—48no—
219C2×C4×C17—22no—
220C2×C4×C17—22no—
221C2×C4×C17—22no—
222C2×C4×C17—22no—
223C2×C4×C17—22no—
224C2×C4×C17—22no—
225C2×C4×C17—44no—
226C2×C4×C17—44no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17—44no—
230C2×C4×C17—44no—
231C2×C4×C17—42no—
232C2×C4×C17#9914yescomplemented
233C2×C4×C17C2×C22⋊C411yescharacteristic
234C2×C4×C17C2×C22⋊C411yescharacteristic
235C2×C4×C17C2×C22⋊C411yescharacteristic
236C2×C4×C17C2×C22⋊C411yescharacteristic
237C22⋊D17—216no—
238C22⋊D17—216no—
239C2×Dic17—24no—
240C2×Dic17—24no—
241C2×Dic17—22no—
242C2×Dic17—22no—
243C2×Dic17—24no—
244C2×Dic17—22no—
245C2×Dic17—42no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—42no—
249C2×Dic17—42no—
250C2×Dic17—42no—
251C2×Dic17C2×C22⋊C412yes—
252C2×Dic17C2×C22⋊C412yes—
253C2×Dic17#11714yescomplemented
254C4×D17—24no—
255C4×D17—24no—
256C4×D17—24no—
257C4×D17—24no—
258C4×D17—42no—
259C4×D17—42no—
260C4×D17—42no—
261C4×D17—42no—
262C22×C4×D4—171no—
263#2280—172no—
264#1819—172no—
265#1799—174no—
266#1781—172no—
267C4×#99—174no—
268C22×C17—28no—
269C22×C17—21no—
270C22×C17—21no—
271C22×C17—21no—
272C22×C17—21no—
273C22×C17—21no—
274C22×C17—21no—
275C22×C17—24no—
276C22×C17—44no—
277C22×C17—44no—
278C22×C17—48no—
279C22×C17—48no—
280C22×C17—42no—
281C22×C17—42no—
282C22×C17C2×#9912yes—
283C22×C17#41012yes—
284C22×C17C22×C22⋊C411yescharacteristic
285C22×C17C2×#11712yes—
286C2×D17—22no—
287C2×D17—22no—
288C2×D17—22no—
289C2×D17—22no—
290C2×D17—22no—
291C2×D17—44no—
292C2×D17—48no—
293C2×D17—48no—
294C2×D17—44no—
295C2×D17#52514yes—
296#595—88no—
297C4×C17—21no—
298C4×C17—21no—
299C4×C17—42no—
300C4×C17C2×#9912yes—
301C4×C17C2×#9912yes—
302Dic17—22no—
303Dic17—22no—
304Dic17—24no—
305Dic17—42no—
306C23×D4—171no—
307C24×C4—171no—
308C24×C4#59511yescharacteristic, complemented
309C2×C4×D4—172no—
310C2×C4×D4—172no—
311C2×C4×D4—172no—
312C2×C4×D4—172no—
313C2×C4×D4—342no—
314C2×C4×D4—342no—
315C2×C4×D4—342no—
316C2×C4×D4—342no—
317C2×#117—342no—
318C22×C4⋊C4—171no—
319C22×C22⋊C4—171no—
320C22×C22⋊C4—171no—
321C22×C42—171no—
322C2×#99—178no—
323#381—342no—
324#380—174no—
325#380—342no—
326#379—174no—
327C4×C22⋊C4—174no—
328C4×C22⋊C4—342no—
329#342—178no—
330C2×C17—22no—
331C2×C17—22no—
332C2×C17—22no—
333C2×C17—44no—
334C2×C17#228011yescharacteristic
335C2×C17C22×#9911yescharacteristic
336C2×C17C2×#41011yescharacteristic
337D17—24no—
338D17—42no—
339C25—171no—
340C25C2×#59511yescharacteristic
341C22×D4—172no—
342C22×D4—172no—
343C22×D4—348no—
344C22×D4—342no—
345C22×D4—342no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—44no—
351C23×C4—171no—
352C23×C4—172no—
353C23×C4—172no—
354C23×C4—172no—
355C23×C4—172no—
356C23×C4—171no—
357C23×C4—171no—
358C23×C4—171no—
359C23×C4—171no—
360C23×C4—171no—
361C23×C4—171no—
362C23×C4—684no—
363C23×C4C2×#59511yescharacteristic
364C23×C4C2×#59512yes—
365C23×C4C2×#59512yes—
366C23×C4C2×#59511yescharacteristic
367C4×D4—344no—
368C4×D4—344no—
369C4×D4—344no—
370C4×D4—344no—
371C4×D4—344no—
372C4×D4—344no—
373C4×D4—344no—
374C4×D4—344no—
375#117—688no—
376C2×C4⋊C4—172no—
377C2×C4⋊C4—172no—
378C2×C4⋊C4—342no—
379C2×C4⋊C4—342no—
380C2×C4⋊C4—344no—
381C2×C22⋊C4—172no—
382C2×C22⋊C4—172no—
383C2×C22⋊C4—172no—
384C2×C22⋊C4—172no—
385C2×C22⋊C4—178no—
386C2×C22⋊C4—342no—
387C2×C22⋊C4—342no—
388C2×C22⋊C4—342no—
389C2×C22⋊C4—342no—
390C2×C22⋊C4—344no—
391C2×C22⋊C4—344no—
392C2×C42—172no—
393C2×C42—172no—
394C2×C42—341no—
395C2×C42—341no—
396C2×C42—341no—
397C2×C42—341no—
398C2×C42—344no—
399#99—3416no—
400#95—344no—
401#95—344no—
402C17#2072211yescharacteristic, complemented, Sylow
403C24—24no—
404C24—21no—
405C24—21no—
406C24—42no—
407C24—42no—
408C24—171no—
409C24—172no—
410C24—172no—
411C24—171no—
412C24—344no—
413C24—682no—
414C24—682no—
415C24C22×#59511yescharacteristic
416C24C22×#59512yes—
417C2×D4—178no—
418C2×D4—344no—
419C2×D4—344no—
420C2×D4—344no—
421C2×D4—344no—
422C2×D4—3416no—
423C2×D4—3416no—
424C2×D4—344no—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—172no—
440C22×C4—172no—
441C22×C4—172no—
442C22×C4—171no—
443C22×C4—171no—
444C22×C4—172no—
445C22×C4—172no—
446C22×C4—172no—
447C22×C4—172no—
448C22×C4—172no—
449C22×C4—172no—
450C22×C4—172no—
451C22×C4—172no—
452C22×C4—172no—
453C22×C4—344no—
454C22×C4—341no—
455C22×C4—341no—
456C22×C4—348no—
457C22×C4—341no—
458C22×C4—341no—
459C22×C4—348no—
460C22×C4—684no—
461C22×C4—684no—
462C22×C4—682no—
463C22×C4—682no—
464C22×C4—682no—
465C22×C4—682no—
466C22×C4—684no—
467C22×C4—682no—
468C22×C4—682no—
469C22×C4C22⋊#59511yescharacteristic
470C22×C4C22⋊#59511yescharacteristic
471C22×C4C22⋊#59511yescharacteristic
472C22×C4C22⋊#59511yescharacteristic
473C22×C4C22×#59511yescharacteristic
474C22×C4C22×#59511yescharacteristic
475C22×C4C22×#59512yes—
476C4⋊C4—344no—
477C4⋊C4—344no—
478C4⋊C4—688no—
479C22⋊C4—344no—
480C22⋊C4—344no—
481C22⋊C4—344no—
482C22⋊C4—344no—
483C22⋊C4—3416no—
484C22⋊C4—688no—
485C22⋊C4—688no—
486C42—342no—
487C42—342no—
488C42—342no—
489C42—342no—
490C42—688no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—24no—
495C23—24no—
496C23—22no—
497C23—22no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—416no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—172no—
506C23—174no—
507C23—172no—
508C23—344no—
509C23—344no—
510C23—344no—
511C23—344no—
512C23—342no—
513C23—682no—
514C23—681no—
515C23—681no—
516C23—682no—
517C23—681no—
518C23—681no—
519C23—6816no—
520C23#1058767714yescomplemented
521C23C2×C22⋊#59511yescharacteristic
522C23C2×C22⋊#59511yescharacteristic
523C23C23×#59511yescharacteristic
524D4—3416no—
525D4—3416no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—172no—
540C2×C4—172no—
541C2×C4—174no—
542C2×C4—344no—
543C2×C4—344no—
544C2×C4—344no—
545C2×C4—342no—
546C2×C4—342no—
547C2×C4—344no—
548C2×C4—344no—
549C2×C4—344no—
550C2×C4—344no—
551C2×C4—342no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4—681no—
558C2×C4—681no—
559C2×C4—682no—
560C2×C4—682no—
561C2×C4—682no—
562C2×C4—688no—
563C2×C4—688no—
564C2×C4—688no—
565C2×C4#1058755114yescomplemented
566C2×C4C2×C22⋊#59511yescharacteristic
567C2×C4C2×C22⋊#59511yescharacteristic
568C2×C4C2×C22⋊#59511yescharacteristic
569C2×C4C2×C22⋊#59511yescharacteristic
570C22—28no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—24no—
578C22—44no—
579C22—48no—
580C22—48no—
581C22—44no—
582C22—42no—
583C22—42no—
584C22—174no—
585C22—342no—
586C22—342no—
587C22—342no—
588C22—342no—
589C22—342no—
590C22—684no—
591C22—688no—
592C22—688no—
593C22—684no—
594C22C2×#1058755112yes—
595C22#1176378812yes—
596C22C22×C22⋊#59511yescharacteristic
597C22C2×#1058767712yes—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—344no—
602C4—342no—
603C4—342no—
604C4—682no—
605C4—1368no—
606C4C2×#1058755112yes—
607C4C2×#1058755112yes—
608C2—22no—
609C2—22no—
610C2—22no—
611C2—44no—
612C2—344no—
613C2—682no—
614C2#1454522811yescharacteristic
615C2C22×#1058755111yescharacteristic
616C2C2×#1176378811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC24×C4×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC23×C22⋊D17C22
cosocleC23×D17C24
hypercenterC24×C4#595
hypocenterC17#20722
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. #14545228C2semidirect
2. #14544679C2semidirect
3. #14544644C2semidirect
5. C4×#10587551C2semidirect
11. #11763751C22semidirect
14. C4×C22⋊#595C22semidirect
15. #11763687C22semidirect
22. C2×C4×C22⋊D17C4semidirect
23. C2×C4×C22⋊D17C4semidirect
26. C22×#63225C4semidirect
27. C22×C22⋊Dic17C4semidirect
29. C22×C4×Dic17C4semidirect
30. C24×C4×C17C4semidirect
199. C23×C17#117semidirect
232. C2×C4×C17#99semidirect
253. C2×Dic17#117semidirect
308. C24×C4#595semidirect
402. C17#20722semidirect
520. C23#10587677semidirect
565. C2×C4#10587551semidirect

Maximal subgroups

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

subgroupindex
#145452282
#145446792
#145446442
#145446102
C4×#105875512
C22×C4×C22⋊D172
#2072217