Finite Group Databasebeta

← #17963690

Subgroups — #17963690

Order 4352.

1346 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
1C2×#11763760C212yesmaximal
2C2×#11763758C212yesmaximal
3#14543970C212yesmaximal
4#14543969C212yesmaximal
5#14543969C212yesmaximal
6#14543964C212yesmaximal
7#14543962C211yesmaximal, characteristic
8#14543960C211yesmaximal, characteristic
9D17×#389C211yesmaximal, characteristic
10C22×C4⋊#595C2212yes—
11C22×C4⋊#595C2212yes—
12C22×C4⋊#595C2212yes—
13C22×C4×#595C2212yes—
14#11763760—28no—
15#11763758—28no—
16C2×(C2×#595)⋊C4C2212yes—
17C2×(C2×#595)⋊C4C2212yes—
18C2×(C2×#595)⋊C4C2212yes—
19C2×(C2×#595)⋊C4C2212yes—
20C2×(C2×#595)⋊C4C2212yes—
21C2×(C2×#595)⋊C4C2211yescharacteristic
22C2×(C2×#595)⋊C4C2212yes—
23C2×(C2×#595)⋊C4C2212yes—
24C2×(C2×#595)⋊C4C2211yescharacteristic
25C2×(C2×#595)⋊C4C2211yescharacteristic
26C2×(C2×#595)⋊C4C2212yes—
27C2×(C2×#595)⋊C4C2211yescharacteristic
28C2×C4⋊C4×D17C2212yes—
29C2×C4⋊C4×D17C2211yescharacteristic
30C2×C4⋊C4×D17C2211yescharacteristic
31C2×C42×D17C2211yescharacteristic
32#11762708C411yescharacteristic, complemented
33#11762707C411yescharacteristic, complemented
34#11762706C412yescomplemented
35#11762705C411yescharacteristic, complemented
36#11762704C412yescomplemented
37#95×D17C2212yes—
38C17×#389C411yescharacteristic, complemented
39C23×#595C2312yes—
40C23×#595C2312yes—
41C23×#595C2312yes—
42C23×#595C2312yes—
43C22×C4×D17C2311yescharacteristic
44C22×C4×D17C2312yes—
45C22×C4×D17C2311yescharacteristic
46C22×C4×D17C2312yes—
47C22×C4×D17C2311yescharacteristic
48C2×C4⋊#595—24no—
49C2×C4⋊#595—24no—
50C2×C4⋊#595—24no—
51C2×C4⋊#595—24no—
52C2×C4⋊#595—24no—
53C2×C4⋊#595—24no—
54C2×C4⋊#595—42no—
55C2×C4⋊#595—42no—
56C2×C4⋊#595—42no—
57C2×C4×#595—24no—
58C2×C4×#595—24no—
59C2×C4×#595—42no—
60C2×C4⋊C4×C17C2×C412yes—
61C2×C4⋊C4×C17C2×C411yescharacteristic
62C2×C4⋊C4×C17C2×C411yescharacteristic
63C2×C42×C17C2×C411yescharacteristic
64C2×C4⋊Dic17C2×C412yes—
65C2×C4⋊Dic17C2×C411yescharacteristic
66C2×C4⋊Dic17C2×C411yescharacteristic
67C2×#63225C2×C412yes—
68C2×#63225C2×C412yes—
69C2×#63225C2×C412yes—
70C2×#63225C2×C412yes—
71C2×C4×Dic17C2×C411yescharacteristic
72C2×C4×Dic17C2×C411yescharacteristic
73C2×C4×Dic17C2×C411yescharacteristic
74C4⋊C4×D17—24no—
75C4⋊C4×D17—24no—
76C4⋊C4×D17—42no—
77C4⋊C4×D17D414yes—
78C4⋊C4×D17Q814yes—
79C42×D17—42no—
80(C2×#595)⋊C4—24no—
81(C2×#595)⋊C4—24no—
82(C2×#595)⋊C4—24no—
83(C2×#595)⋊C4—24no—
84(C2×#595)⋊C4—24no—
85(C2×#595)⋊C4—24no—
86(C2×#595)⋊C4—22no—
87(C2×#595)⋊C4—41no—
88(C2×#595)⋊C4—41no—
89(C2×#595)⋊C4—42no—
90(C2×#595)⋊C4—42no—
91(C2×#595)⋊C4D414yes—
92C17×#95C2×C412yes—
93#10587502C2×C412yes—
94#10587502C2×C412yes—
95#10587502C2×C412yes—
96C23×D17C2411yescharacteristic
97C22×#595—22no—
98C22×#595—22no—
99C22×#595—22no—
100C22×#595—22no—
101C22×#595—22no—
102C22×#595—22no—
103C22×#595—22no—
104C22×#595—22no—
105C22×#595—22no—
106C22×#595—22no—
107C22×#595—22no—
108C22×#595—22no—
109C22×#595—22no—
110C22×#595—22no—
111C22×#595—22no—
112C22×#595—22no—
113C22×#595—22no—
114C22×#595—22no—
115C22×#595—22no—
116C22×#595—22no—
117C22×#595—22no—
118C22×#595—22no—
119C22×#595—22no—
120C22×#595—22no—
121C22×#595—22no—
122C22×#595—22no—
123C22×#595C2×D414yes—
124C22×#595#4114yes—
125C22×C4×C17C22×C411yescharacteristic
126C22×C4×C17C22×C412yes—
127C22×C4×C17C22×C412yes—
128C22×C4×C17C22×C411yescharacteristic
129C22×C4×C17C22×C411yescharacteristic
130C22×Dic17C22×C411yescharacteristic
131C22×Dic17C22×C412yes—
132C22×Dic17C22×C412yes—
133C22×Dic17C22×C411yescharacteristic
134C22×Dic17C22×C411yescharacteristic
135C2×C4×D17—22no—
136C2×C4×D17—22no—
137C2×C4×D17—22no—
138C2×C4×D17—22no—
139C2×C4×D17—22no—
140C2×C4×D17—22no—
141C2×C4×D17—22no—
142C2×C4×D17—22no—
143C2×C4×D17—22no—
144C2×C4×D17—22no—
145C2×C4×D17—22no—
146C2×C4×D17—22no—
147C2×C4×D17—22no—
148C2×C4×D17—21no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—22no—
152C2×C4×D17—21no—
153C2×C4×D17C2×D414yes—
154C2×C4×D17C2×D412yes—
155C2×C4×D17C2×D412yes—
156C2×C4×D17C2×Q812yes—
157C2×C4×D17C2×Q814yes—
158C2×C4×D17#4112yes—
159C4⋊#595—48no—
160C4⋊#595—48no—
161C4⋊#595—48no—
162C4×#595—48no—
163C4⋊C4×C17—24no—
164C4⋊C4×C17—41no—
165C4⋊C4×C17C4⋊C414yescomplemented
166C42×C17—41no—
167C4⋊Dic17—24no—
168C4⋊Dic17—41no—
169C4⋊Dic17C4⋊C414yescomplemented
170#63225—24no—
171#63225—24no—
172#63225—42no—
173#63225C4⋊C418yescomplemented
174C4×Dic17—41no—
175C4×Dic17—41no—
176C4×Dic17—41no—
177#14439—171nomaximal, Sylow
178C23×C17C23×C411yescharacteristic
179C22×D17C22×D411yescharacteristic
180C22×D17C22×D411yescharacteristic
181C22×D17C22×Q811yescharacteristic
182C22×D17C2×#4112yes—
183C22×D17C2×#4111yescharacteristic
184C22×D17H(5,𝔽2)12yes—
185C22×D17H(5,𝔽2)11yescharacteristic
186C22×D172−1+412yes—
187C22×D172−1+412yes—
188C22×D172−1+411yescharacteristic
189C2×#595—24no—
190C2×#595—24no—
191C2×#595—24no—
192C2×#595—24no—
193C2×#595—24no—
194C2×#595—24no—
195C2×#595—42no—
196C2×#595—42no—
197C2×#595—42no—
198C2×#595—42no—
199C2×#595—42no—
200C2×#595—42no—
201C2×#595—42no—
202C2×#595—42no—
203C2×#595—42no—
204C2×#595—42no—
205C2×#595—42no—
206C2×#595—42no—
207C2×#595—42no—
208C2×#595—42no—
209C2×#595—42no—
210C2×#595—42no—
211C2×#595—42no—
212C2×#595—42no—
213C2×#595—42no—
214C2×#595—42no—
215C2×#595—42no—
216C2×#595—42no—
217C2×C4×C17—22no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—22no—
223C2×C4×C17—22no—
224C2×C4×C17—22no—
225C2×C4×C17—21no—
226C2×C4×C17—22no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17C2×C4⋊C414yes—
230C2×C4×C17C2×C4⋊C412yes—
231C2×C4×C17C4×D412yes—
232C2×Dic17—22no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—22no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—21no—
241C2×Dic17—22no—
242C2×Dic17—21no—
243C2×Dic17—21no—
244C2×Dic17C2×C4⋊C412yes—
245C2×Dic17C2×C4⋊C414yes—
246C2×Dic17C4×D412yes—
247C4×D17—24no—
248C4×D17—24no—
249C4×D17—24no—
250C4×D17—24no—
251C4×D17—24no—
252C4×D17—24no—
253C4×D17—24no—
254C4×D17—24no—
255C4×D17—42no—
256C4×D17—42no—
257C4×D17—42no—
258C4×D17—42no—
259C4×D17—42no—
260C4×D17—42no—
261C2×#389—171no—
262C2×#389—172no—
263C2×#387—172no—
264#1442—172no—
265#1441—172no—
266#1441—172no—
267#1436—172no—
268C4⋊#95—171no—
269#1434—171no—
270C22×C17C22×C4⋊C411yescharacteristic
271C22×C17C2×C4×D411yescharacteristic
272C22×C17C4×#4111yescharacteristic
273C22×C17#51811yescharacteristic
274C22×C17#51911yescharacteristic
275C22×C17#51911yescharacteristic
276C22×C17#52011yescharacteristic
277C2×D17#53612yes—
278C2×D17#53712yes—
279C2×D17#53912yes—
280C2×D17#54112yes—
281C2×D17#54112yes—
282C2×D17#54412yes—
283C2×D17D4211yescharacteristic
284C2×D17#54612yes—
285C2×D17#54711yescharacteristic
286C2×D17#54812yes—
287C2×D17D4×Q811yescharacteristic
288C2×D17#55312yes—
289C2×D17#55411yescharacteristic
290C2×D17#55712yes—
291C2×D17#56212yes—
292C2×D17#56312yes—
293#595—44no—
294#595—44no—
295#595—82no—
296#595—82no—
297C4×C17—22no—
298C4×C17—24no—
299C4×C17—22no—
300C4×C17—42no—
301C4×C17—41no—
302Dic17—22no—
303Dic17—24no—
304Dic17—22no—
305Dic17—42no—
306Dic17—41no—
307C22×C4⋊C4—171no—
308C22×C4⋊C4—172no—
309C22×C4⋊C4—171no—
310C22×C4⋊C4—172no—
311C22×C4⋊C4—172no—
312C22×C4⋊C4—172no—
313C22×C42—171no—
314C22×C42—172no—
315#389—172no—
316#389—171no—
317#389—171no—
318#389—171no—
319#389—172no—
320#389—348no—
321#389#59511yescharacteristic, complemented
322#387—348no—
323C2×#95—171no—
324C2×#95—172no—
325C2×#95—171no—
326C2×#95—172no—
327C2×#95—172no—
328C2×#95—172no—
329C2×#95—172no—
330C2×#95—172no—
331C2×#95—172no—
332C2×#95—172no—
333C2×#95—171no—
334C2×#95—171no—
335C2×#95—172no—
336C2×C17#231611yescharacteristic
337C2×C17#232711yescharacteristic
338C2×C17#233611yescharacteristic
339C2×C17D4×C4⋊C411yescharacteristic
340C2×C17#235111yescharacteristic
341C2×C17#236411yescharacteristic
342C2×C17#237811yescharacteristic
343D17#268112yes—
344D17#271312yes—
345D17#272512yes—
346D17#280212yes—
347C23×C4—171no—
348C23×C4—172no—
349C23×C4—171no—
350C23×C4—172no—
351C23×C4—172no—
352C23×C4—172no—
353C23×C4—171no—
354C23×C4—172no—
355C23×C4—172no—
356C2×C4⋊C4—172no—
357C2×C4⋊C4—171no—
358C2×C4⋊C4—174no—
359C2×C4⋊C4—174no—
360C2×C4⋊C4—172no—
361C2×C4⋊C4—172no—
362C2×C4⋊C4—172no—
363C2×C4⋊C4—172no—
364C2×C4⋊C4—171no—
365C2×C4⋊C4—344no—
366C2×C4⋊C4—344no—
367C2×C4⋊C4—344no—
368C2×C4⋊C4—344no—
369C2×C4⋊C4—344no—
370C2×C4⋊C4—344no—
371C2×C4⋊C4—344no—
372C2×C4⋊C4—344no—
373C2×C4⋊C4—682no—
374C2×C4⋊C4—682no—
375C2×C4⋊C4—682no—
376C2×C4⋊C4—682no—
377C2×C4⋊C4C2×#59512yes—
378C2×C4⋊C4C2×#59511yescharacteristic
379C2×C4⋊C4C2×#59511yescharacteristic
380C2×C42—171no—
381C2×C42—171no—
382C2×C42—171no—
383C2×C42—344no—
384C2×C42—344no—
385C2×C42—682no—
386C2×C42—682no—
387C2×C42C2×#59511yescharacteristic
388#95—174no—
389#95—172no—
390#95—172no—
391#95—172no—
392#95—344no—
393#95—344no—
394#95—344no—
395#95—344no—
396#95—344no—
397#95—342no—
398#95—344no—
399#95—681no—
400#95—681no—
401#95—682no—
402#95—682no—
403#95C2×#59512yes—
404C17#1443911yescharacteristic, complemented, Sylow
405C24—171no—
406C22×C4—172no—
407C22×C4—171no—
408C22×C4—171no—
409C22×C4—172no—
410C22×C4—174no—
411C22×C4—174no—
412C22×C4—172no—
413C22×C4—172no—
414C22×C4—172no—
415C22×C4—174no—
416C22×C4—174no—
417C22×C4—171no—
418C22×C4—172no—
419C22×C4—342no—
420C22×C4—342no—
421C22×C4—342no—
422C22×C4—342no—
423C22×C4—342no—
424C22×C4—342no—
425C22×C4—342no—
426C22×C4—342no—
427C22×C4—342no—
428C22×C4—342no—
429C22×C4—341no—
430C22×C4—342no—
431C22×C4—342no—
432C22×C4—342no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—342no—
436C22×C4—341no—
437C22×C4—342no—
438C22×C4—342no—
439C22×C4—342no—
440C22×C4—342no—
441C22×C4—342no—
442C22×C4—342no—
443C22×C4—342no—
444C22×C4—342no—
445C22×C4—342no—
446C22×C4—342no—
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—342no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4C22×#59511yescharacteristic
464C22×C4C22×#59512yes—
465C22×C4C22×#59512yes—
466C22×C4C22×#59511yescharacteristic
467C22×C4C22×#59511yescharacteristic
468C4⋊C4—24no—
469C4⋊C4—41no—
470C4⋊C4—178no—
471C4⋊C4—174no—
472C4⋊C4—344no—
473C4⋊C4—344no—
474C4⋊C4—344no—
475C4⋊C4—682no—
476C4⋊C4—681no—
477C4⋊C4—688no—
478C4⋊C4—688no—
479C4⋊C4—688no—
480C4⋊C4C4⋊#59514yescomplemented
481C42—41no—
482C42—681no—
483C42—681no—
484C42—681no—
485C42—688no—
486C23—171no—
487C23—171no—
488C23—171no—
489C23—171no—
490C23—172no—
491C23—172no—
492C23—172no—
493C23—172no—
494C23—171no—
495C23—171no—
496C23C23×#59511yescharacteristic
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—172no—
510C2×C4—174no—
511C2×C4—172no—
512C2×C4—344no—
513C2×C4—344no—
514C2×C4—344no—
515C2×C4—344no—
516C2×C4—344no—
517C2×C4—344no—
518C2×C4—344no—
519C2×C4—344no—
520C2×C4—342no—
521C2×C4—341no—
522C2×C4—341no—
523C2×C4—341no—
524C2×C4—341no—
525C2×C4—342no—
526C2×C4—344no—
527C2×C4—344no—
528C2×C4—344no—
529C2×C4—344no—
530C2×C4—344no—
531C2×C4—344no—
532C2×C4—342no—
533C2×C4—342no—
534C2×C4—341no—
535C2×C4—342no—
536C2×C4—341no—
537C2×C4—341no—
538C2×C4—682no—
539C2×C4—682no—
540C2×C4—682no—
541C2×C4—682no—
542C2×C4—682no—
543C2×C4—682no—
544C2×C4—682no—
545C2×C4—682no—
546C2×C4—682no—
547C2×C4—682no—
548C2×C4—682no—
549C2×C4—682no—
550C2×C4—682no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4—682no—
558C2×C4—682no—
559C2×C4—682no—
560C2×C4—682no—
561C2×C4—682no—
562C2×C4—682no—
563C2×C4—682no—
564C2×C4—682no—
565C2×C4—682no—
566C2×C4C2×C4⋊#59512yes—
567C2×C4C2×C4⋊#59514yes—
568C2×C4D4×#59512yes—
569C22—172no—
570C22—172no—
571C22—172no—
572C22—172no—
573C22—172no—
574C22—172no—
575C22—171no—
576C22—171no—
577C22—171no—
578C22—171no—
579C22—172no—
580C22—172no—
581C22—172no—
582C22—172no—
583C22—172no—
584C22—172no—
585C22C22×C4⋊#59511yescharacteristic
586C22C2×D4×#59511yescharacteristic
587C22#41×#59511yescharacteristic
588C22#1176387611yescharacteristic
589C22#1176387711yescharacteristic
590C22#1176387711yescharacteristic
591C22#1176387811yescharacteristic
592C4—22no—
593C4—24no—
594C4—22no—
595C4—42no—
596C4—41no—
597C4—342no—
598C4—344no—
599C4—342no—
600C4—684no—
601C4—684no—
602C4—682no—
603C4—681no—
604C4—1362no—
605C4—1362no—
606C2—172no—
607C2—172no—
608C2—172no—
609C2—172no—
610C2#1454526411yescharacteristic
611C2#1454527511yescharacteristic
612C2#1454528411yescharacteristic
613C2D4×C4⋊#59511yescharacteristic
614C2#1454529911yescharacteristic
615C2#1454531211yescharacteristic
616C2#1454532611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutator, socleC23×C17C23×C4
FittingC17×#389C4
prime radical, cosocleC23×D17C24
hypercenter#389#595
hypocenterC17#14439
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
32. #11762708C4semidirect
33. #11762707C4semidirect
34. #11762706C4semidirect
35. #11762705C4semidirect
36. #11762704C4semidirect
38. C17×#389C4semidirect
165. C4⋊C4×C17C4⋊C4semidirect
169. C4⋊Dic17C4⋊C4semidirect
173. #63225C4⋊C4semidirect
321. #389#595semidirect
404. C17#14439semidirect
480. C4⋊C4C4⋊#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637602
C2×#117637582
#145439702
#145439692
#145439642
#145439622
#145439602
D17×#3892
#1443917