Finite Group Databasebeta

← #17034274

Subgroups — #17034274

Order 4352.

1318 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763288C211yesmaximal, characteristic
2#14531384C212yesmaximal, complemented
3#14528860C212yesmaximal, complemented
4#14528771C212yesmaximal, complemented
5#14528770C212yesmaximal, complemented
6#14528700C212yesmaximal
7C4×#10587477C212yesmaximal, complemented
8C4×#10587505C211yesmaximal, characteristic, complemented
9C4×C17×#99C211yesmaximal, characteristic, complemented
10C22×#63254C2211yescharacteristic
11#11763288—24no—
12#11763288—24no—
13C2×C4×Dic34C411yescharacteristic, complemented
14C2×#10587573C411yescharacteristic, complemented
15C2×D4×Dic17C2211yescharacteristic
16C2×C4×C22⋊D17C411yescharacteristic, complemented
17C2×C4×C22⋊D17C2211yescharacteristic
18C2×#10587567C411yescharacteristic, complemented
19C2×#10587567C2211yescharacteristic
20C2×#10587558C411yescharacteristic, complemented
21C2×#10587563C411yescharacteristic, complemented
22C2×#10587563C2211yescharacteristic
23C22×#63225C411yescharacteristic, complemented
24C22×#63225C2211yescharacteristic
25C2×C4⋊C4×D17C411yescharacteristic, complemented
26C2×#10587505C2212yes—
27C2×#10587477C2214yes—
28#11762693—24no—
29#11762691—24no—
30#11762670C2214yes—
31#11762667C2214yes—
32C4×C22⋊Dic17C2212yes—
33#11762576C2212yes—
34#11762575C2214yes—
35C2×C4×D4×C17C2211yescharacteristic
36C2×C17×#99C2212yes—
37C4×C22⋊C4×C17C2212yes—
38C17×#342C2212yes—
39C22×D4×C17C2311yescharacteristic
40C23×C4×C17C2×C411yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C22×C22⋊D17C2×C411yescharacteristic
43C22×C22⋊D17C2311yescharacteristic
44C23×Dic17C2×C411yescharacteristic
45C23×Dic17C2×C411yescharacteristic
46C23×Dic17C2311yescharacteristic
47C23×Dic17C2311yescharacteristic
48C2×#63254—24no—
49C2×#63254—24no—
50C2×#63254—24no—
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×Dic34C2×C411yescharacteristic
55C4×D4×C17—22no—
56C4×D4×C17—22no—
57C2×C4⋊C4×C17C2×C411yescharacteristic
58C2×C22⋊C4×C17C2×C411yescharacteristic
59C2×C22⋊C4×C17C2314yes—
60C2×C22⋊C4×C17C2311yescharacteristic
61C2×C42×C17—22no—
62C2×C42×C17C2×C411yescharacteristic
63C2×C22⋊Dic17C2×C411yescharacteristic
64C2×C22⋊Dic17C2314yes—
65C2×C22⋊Dic17C2311yescharacteristic
66D4×Dic17—24no—
67C4×C22⋊D17—22no—
68C4×C22⋊D17—22no—
69C4×C22⋊D17—22no—
70C4×C22⋊D17—22no—
71C2×#63227C2×C411yescharacteristic
72C2×#63227C2×C411yescharacteristic
73C2×C4⋊Dic17C2×C411yescharacteristic
74C2×#63225—22no—
75C2×#63225—22no—
76C2×#63225—24no—
77C2×#63225C2×C411yescharacteristic
78C2×#63225C2×C411yescharacteristic
79C2×#63225C2×C411yescharacteristic
80C2×#63225C2×C411yescharacteristic
81C2×#63225C2×C411yescharacteristic
82C2×#63225C2×C411yescharacteristic
83C2×#63225C2×C411yescharacteristic
84C2×#63225C2×C411yescharacteristic
85C2×#63225D414yes—
86C2×#63225D414yes—
87C2×C4×Dic17—22no—
88C2×C4×Dic17C2×C411yescharacteristic
89C2×C4×Dic17C2×C411yescharacteristic
90C2×C4×Dic17C2×C411yescharacteristic
91C2×C4×Dic17C2×C411yescharacteristic
92C2×C4×Dic17C2×C411yescharacteristic
93C4⋊C4×D17—24no—
94#10587573—24no—
95#10587567—24no—
96#10587567—24no—
97#10587563—24no—
98#10587563—24no—
99#10587558—22no—
100#10587558—22no—
101C4×Dic34—22no—
102C4×Dic34—22no—
103C17×#99—24no—
104C17×#95—22no—
105#10587505—24no—
106#10587502—22no—
107#10587502—24no—
108#10587502—28no—
109#10587477—28no—
110C24×C17C22×C411yescharacteristic
111C24×C17C2411yescharacteristic
112C23×D17C22×C411yescharacteristic
113C2×D4×C17—22no—
114C2×D4×C17—22no—
115C2×D4×C17#4114yes—
116C22×C4×C17—21no—
117C22×C4×C17—21no—
118C22×C4×C17—24no—
119C22×C4×C17—81no—
120C22×C4×C17—81no—
121C22×C4×C17C22×C411yescharacteristic
122C22×C4×C17C22×C411yescharacteristic
123C22×C4×C17C22×C411yescharacteristic
124C22×C4×C17C22×C411yescharacteristic
125C22×C4×C17C22×C411yescharacteristic
126C22×C4×C17C2×D412yes—
127C22×C4×C17C2×D412yes—
128C2×C22⋊D17—22no—
129C2×C22⋊D17—22no—
130C2×C22⋊D17—22no—
131C2×C22⋊D17—22no—
132C2×C22⋊D17—22no—
133C2×C22⋊D17#4114yes—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—24no—
141C22×Dic17—81no—
142C22×Dic17—81no—
143C22×Dic17C22×C411yescharacteristic
144C22×Dic17C22×C411yescharacteristic
145C22×Dic17C22×C411yescharacteristic
146C22×Dic17C22×C411yescharacteristic
147C22×Dic17C22×C411yescharacteristic
148C22×Dic17C22×C411yescharacteristic
149C22×Dic17C22×C411yescharacteristic
150C22×Dic17C2×D414yes—
151C22×Dic17C2×D414yes—
152#63254—232no—
153C2×C4×D17—22no—
154C2×C4×D17—22no—
155C2×C4×D17—22no—
156C2×C4×D17—22no—
157C2×C4×D17—22no—
158C2×C4×D17—81no—
159C2×C4×D17—81no—
160C2×Dic34—22no—
161C2×Dic34—22no—
162C2×Dic34—22no—
163C4⋊C4×C17—22no—
164C22⋊C4×C17—22no—
165C22⋊C4×C17—22no—
166C22⋊C4×C17—24no—
167C22⋊C4×C17—24no—
168C42×C17—21no—
169C42×C17—21no—
170C42×C17—82no—
171C22⋊Dic17—22no—
172C22⋊Dic17—22no—
173C22⋊Dic17—24no—
174C22⋊Dic17—24no—
175#63227—21no—
176#63227—21no—
177#63227—22no—
178C4⋊Dic17—22no—
179#63225—21no—
180#63225—21no—
181#63225—22no—
182#63225—22no—
183#63225—22no—
184#63225—84no—
185#63225C22⋊C412yes—
186#63225C22⋊C412yes—
187#63225C22⋊C412yes—
188#63225C22⋊C412yes—
189#63225C22⋊C414yes—
190#63225C22⋊C414yes—
191C4×Dic17—22no—
192C4×Dic17—22no—
193C4×Dic17—22no—
194C4×Dic17—22no—
195C4×Dic17—22no—
196C4×Dic17—82no—
197#20725—171nomaximal, Sylow
198C23×C17—21no—
199C23×C17—21no—
200C23×C17—41no—
201C23×C17—41no—
202C23×C17—41no—
203C23×C17—41no—
204C23×C17#11712yes—
205C23×C17C23×C411yescharacteristic
206C23×C17C22×D412yes—
207C23×C17C2×#4112yes—
208C23×C17C2×#4112yes—
209C22×D17—21no—
210C22×D17—21no—
211C22×D17—41no—
212C22×D17—41no—
213C22×D17#11712yes—
214D4×C17—28no—
215C2×C4×C17—21no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—42no—
220C2×C4×C17—41no—
221C2×C4×C17—41no—
222C2×C4×C17—42no—
223C2×C4×C17—41no—
224C2×C4×C17—41no—
225C2×C4×C17—44no—
226C2×C4×C17—44no—
227C2×C4×C17—44no—
228C2×C4×C17—81no—
229C2×C4×C17—81no—
230C2×C4×C17C2×C22⋊C411yescharacteristic
231C2×C4×C17C2×C22⋊C411yescharacteristic
232C2×C4×C17C2×C22⋊C412yes—
233C2×C4×C17#11712yes—
234C22⋊D17—28no—
235C22⋊D17—28no—
236C2×Dic17—28no—
237C2×Dic17—21no—
238C2×Dic17—21no—
239C2×Dic17—21no—
240C2×Dic17—21no—
241C2×Dic17—21no—
242C2×Dic17—21no—
243C2×Dic17—28no—
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—44no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—44no—
252C2×Dic17—44no—
253C2×Dic17—44no—
254C2×Dic17—82no—
255C2×Dic17C2×C22⋊C412yes—
256C2×Dic17C2×C22⋊C412yes—
257C2×Dic17C2×C22⋊C412yes—
258C2×Dic17C2×C22⋊C412yes—
259C2×Dic17#11712yes—
260C4×D17—28no—
261C4×D17—82no—
262C4×D17—82no—
263Dic34—28no—
264C2×#520—171no—
265#2313—172no—
266#1820—172no—
267#1799—172no—
268#1799—172no—
269#1782—172no—
270C4×#99—172no—
271C4×#99—171no—
272C4×#99D1711yescharacteristic, complemented
273C22×C17—22no—
274C22×C17—21no—
275C22×C17—22no—
276C22×C17—21no—
277C22×C17—22no—
278C22×C17—42no—
279C22×C17—42no—
280C22×C17—42no—
281C22×C17—42no—
282C22×C17—41no—
283C22×C17—41no—
284C22×C17C22×C22⋊C411yescharacteristic
285C22×C17C2×#11711yescharacteristic
286C22×C17C2×#11711yescharacteristic
287C22×C17#52514yes—
288C2×D17—22no—
289C2×D17—42no—
290C2×D17—41no—
291C2×D17—41no—
292C2×D17—42no—
293C4×C17—22no—
294C4×C17—21no—
295C4×C17—21no—
296C4×C17—22no—
297C4×C17—41no—
298C4×C17—41no—
299C4×C17—84no—
300Dic17—22no—
301Dic17—22no—
302Dic17—22no—
303Dic17—22no—
304Dic17—22no—
305Dic17—41no—
306Dic17—41no—
307Dic17—84no—
308C22×#41—171no—
309#520—344no—
310#520—344no—
311C2×C4×Q8—171no—
312C2×C4×Q8—171no—
313C2×C4×D4—171no—
314C2×C4×D4—171no—
315C2×C4×D4—171no—
316C2×C4×D4—171no—
317C2×C4×D4—171no—
318C2×C4×D4C2×D1711yescharacteristic
319C2×#117—171no—
320C2×#117—171no—
321C2×#117—171no—
322C22×C4⋊C4—171no—
323C22×C4⋊C4—171no—
324C22×C4⋊C4—171no—
325C2×#99—172no—
326C2×#99—174no—
327C2×#99C2×D1712yes—
328#387—344no—
329#387—344no—
330#381—174no—
331#380—174no—
332C4×C22⋊C4—172no—
333C4×C22⋊C4C2×D1712yes—
334#342—174no—
335#342—172no—
336#342C2×D1712yes—
337C2×C17—24no—
338C2×C17—21no—
339C2×C17—21no—
340C2×C17—42no—
341C2×C17#228011yescharacteristic
342C2×C17#288311yescharacteristic
343C2×C17#288411yescharacteristic
344D17—42no—
345C2×#41—344no—
346C2×#41—344no—
347C2×#41—344no—
348C22×Q8—171no—
349C22×D4—171no—
350C22×D4—171no—
351C22×D4C22×D1711yescharacteristic
352C23×C4—171no—
353C23×C4—171no—
354C23×C4—171no—
355C23×C4—171no—
356C23×C4—171no—
357C23×C4—171no—
358C23×C4—171no—
359C23×C4C4×D1711yescharacteristic
360C23×C4C22×D1711yescharacteristic
361C4×Q8—342no—
362C4×Q8—342no—
363C4×Q8—344no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—344no—
367C4×D4—344no—
368C4×D4—342no—
369C4×D4—342no—
370C4×D4—344no—
371C4×D4—342no—
372C4×D4—342no—
373#117—342no—
374#117—342no—
375#117—344no—
376#117—344no—
377C2×C4⋊C4—171no—
378C2×C4⋊C4—171no—
379C2×C4⋊C4—171no—
380C2×C4⋊C4—171no—
381C2×C4⋊C4—174no—
382C2×C4⋊C4—174no—
383C2×C4⋊C4—171no—
384C2×C4⋊C4—171no—
385C2×C4⋊C4—171no—
386C2×C4⋊C4—171no—
387C2×C4⋊C4—171no—
388C2×C4⋊C4—344no—
389C2×C4⋊C4—342no—
390C2×C4⋊C4—342no—
391C2×C4⋊C4—344no—
392C2×C4⋊C4C4×D1711yescharacteristic
393C2×C22⋊C4—171no—
394C2×C22⋊C4—171no—
395C2×C22⋊C4—171no—
396C2×C22⋊C4—171no—
397C2×C22⋊C4—174no—
398C2×C22⋊C4C4×D1711yescharacteristic
399C2×C22⋊C4C22×D1714yes—
400C2×C22⋊C4C22×D1711yescharacteristic
401C2×C42—22no—
402C2×C42—171no—
403C2×C42—171no—
404C2×C42—171no—
405C2×C42—171no—
406C2×C42—171no—
407C2×C42—342no—
408C2×C42C4×D1711yescharacteristic
409#99—24no—
410#99—348no—
411#99—344no—
412#95—22no—
413#95—344no—
414#95—348no—
415#95—342no—
416C17#2072511yescharacteristic, complemented, Sylow
417C24—171no—
418C24C2×C4×D1711yescharacteristic
419C24C23×D1711yescharacteristic
420#41—3432no—
421C2×Q8—342no—
422C2×Q8—342no—
423C2×Q8—342no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—174no—
427C2×D4—342no—
428C2×D4—342no—
429C2×D4—342no—
430C2×D4—342no—
431C2×D4—342no—
432C2×D4#6325214yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—81no—
437C22×C4—81no—
438C22×C4—171no—
439C22×C4—171no—
440C22×C4—171no—
441C22×C4—174no—
442C22×C4—171no—
443C22×C4—171no—
444C22×C4—174no—
445C22×C4—171no—
446C22×C4—171no—
447C22×C4—342no—
448C22×C4—342no—
449C22×C4—342no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—342no—
453C22×C4—342no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—342no—
457C22×C4—342no—
458C22×C4—344no—
459C22×C4—1361no—
460C22×C4—1361no—
461C22×C4—1361no—
462C22×C4—1361no—
463C22×C4C2×C4×D1711yescharacteristic
464C22×C4C2×C4×D1711yescharacteristic
465C22×C4C2×C4×D1711yescharacteristic
466C22×C4C2×C4×D1711yescharacteristic
467C22×C4C2×C4×D1711yescharacteristic
468C22×C4D4×D1712yes—
469C22×C4D4×D1712yes—
470C4⋊C4—22no—
471C4⋊C4—172no—
472C4⋊C4—172no—
473C4⋊C4—174no—
474C4⋊C4—172no—
475C4⋊C4—172no—
476C4⋊C4—174no—
477C4⋊C4—342no—
478C4⋊C4—342no—
479C4⋊C4—342no—
480C4⋊C4—342no—
481C4⋊C4—341no—
482C4⋊C4—341no—
483C4⋊C4—1364no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—342no—
489C22⋊C4—342no—
490C22⋊C4—342no—
491C22⋊C4—341no—
492C22⋊C4—341no—
493C22⋊C4—344no—
494C22⋊C4—344no—
495C42—21no—
496C42—21no—
497C42—82no—
498C42—342no—
499C42—342no—
500C42—342no—
501C42—342no—
502C42—342no—
503C42—1362no—
504C23—21no—
505C23—21no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—172no—
511C23—341no—
512C23—341no—
513C23—681no—
514C23—681no—
515C23#1058755812yes—
516C23C22×C4×D1711yescharacteristic
517C23C2×#6325212yes—
518C23C2×D4×D1712yes—
519C23#41×D1712yes—
520Q8—348no—
521D4—28no—
522D4—348no—
523D4—348no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—172no—
540C2×C4—172no—
541C2×C4—172no—
542C2×C4—172no—
543C2×C4—172no—
544C2×C4—348no—
545C2×C4—348no—
546C2×C4—341no—
547C2×C4—341no—
548C2×C4—341no—
549C2×C4—341no—
550C2×C4—341no—
551C2×C4—341no—
552C2×C4—348no—
553C2×C4—341no—
554C2×C4—341no—
555C2×C4—684no—
556C2×C4—681no—
557C2×C4—681no—
558C2×C4—681no—
559C2×C4—681no—
560C2×C4—684no—
561C2×C4—684no—
562C2×C4—684no—
563C2×C4—1362no—
564C2×C4—1362no—
565C2×C4—1362no—
566C2×C4#1058755812yes—
567C2×C4C22⋊C4×D1711yescharacteristic
568C2×C4C22⋊C4×D1711yescharacteristic
569C2×C4C22⋊C4×D1712yes—
570C22—22no—
571C22—21no—
572C22—22no—
573C22—21no—
574C22—22no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22—41no—
581C22—342no—
582C22—682no—
583C22—682no—
584C22—681no—
585C22—681no—
586C22C2×C22⋊C4×D1711yescharacteristic
587C22#117×D1711yescharacteristic
588C22C2×#1058755811yescharacteristic
589C22#1176331814yes—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—84no—
597C4—342no—
598C4—342no—
599C4—342no—
600C4—342no—
601C4—342no—
602C4—681no—
603C4—681no—
604C4—1364no—
605C2—24no—
606C2—21no—
607C2—21no—
608C2—42no—
609C2—682no—
610C2#1453116511yescharacteristic
611C2#1453724211yescharacteristic
612C2#1453724611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC4×C17×#99C2
socleC22×C17C22×C22⋊C4
prime radicalC22×#63254C22
cosocleC24×C17C24
hypercenterC4×#99D17
hypocenterC17#20725
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #14531384C2semidirect
3. #14528860C2semidirect
4. #14528771C2semidirect
5. #14528770C2semidirect
7. C4×#10587477C2semidirect
8. C4×#10587505C2semidirect
9. C4×C17×#99C2semidirect
13. C2×C4×Dic34C4semidirect
14. C2×#10587573C4semidirect
16. C2×C4×C22⋊D17C4semidirect
18. C2×#10587567C4semidirect
20. C2×#10587558C4semidirect
21. C2×#10587563C4semidirect
23. C22×#63225C4semidirect
25. C2×C4⋊C4×D17C4semidirect
272. C4×#99D17semidirect
416. C17#20725semidirect

Maximal subgroups

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

subgroupindex
C2×#117632882
#145313842
#145288602
#145287712
#145287702
#145287002
C4×#105874772
C4×#105875052
C4×C17×#992
#2072517