Finite Group Databasebeta

← #17950950

Subgroups — #17950950

Order 4352.

1130 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763777C211yesmaximal, characteristic
2C2×#11763751C211yesmaximal, characteristic
3#14543646C214yesmaximal, complemented
4D17×#380C211yesmaximal, characteristic
5C22×#63242C412yescomplemented
6C22×C4⋊#595—21no—
7C22×C22⋊#595—21no—
8C2×#10587543—21no—
9#11763777—21no—
10#11763777—21no—
11#11763777C412yescomplemented
12#11763777C2212yes—
13C2×C22⋊#3624—21no—
14#11763751—21no—
15#11763751—21no—
16#11763751C412yescomplemented
17#11763751C2212yes—
18C2×(C2×#595)⋊C4C412yescomplemented
19C23×C4×D17C2211yescharacteristic
20C2×C4⋊C4×D17—21no—
21C2×C22⋊C4×D17—21no—
22#11762669C411yescharacteristic, complemented
23#11762668C2212yes—
24#11762667—21no—
25#11762666—21no—
26#95×D17C412yescomplemented
27C17×#380C411yescharacteristic, complemented
28C24×D17D411yescharacteristic
29C23×#595—22no—
30C23×C4×C17C2×C411yescharacteristic
31C23×Dic17D411yescharacteristic
32C22×C4×D17—22no—
33C22×C4×D17—44no—
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×D17Q811yescharacteristic
44C22×C4×D17Q811yescharacteristic
45C22×C4×D17C2311yescharacteristic
46C2×C22⋊#595—22no—
47C2×C22⋊#595—22no—
48C2×C22⋊#595—42no—
49C2×C22⋊#595—42no—
50C22×#3624—22no—
51C2×C4⋊#595—22no—
52C2×C4⋊#595—22no—
53C2×C4⋊#595—44no—
54C2×#63242—22no—
55C2×#63242—44no—
56C2×#63242C2×C414yescomplemented
57C2×C4⋊C4×C17—21no—
58C2×C22⋊C4×C17—21no—
59C2×C22⋊Dic17—21no—
60C2×#63227—22no—
61C2×C4⋊Dic17—21no—
62C2×#63225—22no—
63C4⋊C4×D17—44no—
64C22⋊C4×D17—42no—
65C22⋊C4×D17—42no—
66C22⋊#3624—22no—
67C22⋊#3624—22no—
68(C2×#595)⋊C4—22no—
69(C2×#595)⋊C4C2×C414yescomplemented
70#10587543—22no—
71#10587543—22no—
72C17×#95C2×C412yescomplemented
73#10587502—22no—
74#10587502C2×C412yescomplemented
75C24×C17C22⋊C411yescharacteristic
76C23×D17—42no—
77C23×D17—42no—
78C23×D17C22⋊C411yescharacteristic
79C23×D17C22⋊C411yescharacteristic
80C23×D17C22⋊C411yescharacteristic
81C23×D17C4⋊C411yescharacteristic
82C23×D17C4⋊C411yescharacteristic
83C23×D17D812yes—
84C23×D17SD1612yes—
85C23×D17SD1612yes—
86C23×D17Q1612yes—
87C23×D17C2×D411yescharacteristic
88C22×#595—24no—
89C22×#595—44no—
90C22×#595—44no—
91C22×#595—44no—
92C22×C4×C17—22no—
93C22×C4×C17—42no—
94C22×C4×C17C4211yescharacteristic
95C22×C4×C17C4211yescharacteristic
96C22×C4×C17C22⋊C411yescharacteristic
97C22×C4×C17C4⋊C411yescharacteristic
98C22×C4×C17C4⋊C411yescharacteristic
99C22×C4×C17C22×C411yescharacteristic
100C22×Dic17—22no—
101C22×Dic17—42no—
102C22×Dic17C22⋊C411yescharacteristic
103C22×Dic17C22⋊C411yescharacteristic
104C22×Dic17C22⋊C411yescharacteristic
105C22×Dic17C4⋊C411yescharacteristic
106C22×Dic17C4⋊C411yescharacteristic
107C22×Dic17C2×D411yescharacteristic
108C2×C4×D17—24no—
109C2×C4×D17—24no—
110C2×C4×D17—24no—
111C2×C4×D17—42no—
112C2×C4×D17—42no—
113C2×C4×D17—42no—
114C2×C4×D17—42no—
115C2×C4×D17—42no—
116C2×C4×D17—42no—
117C2×C4×D17—42no—
118C2×C4×D17—42no—
119C2×C4×D17—42no—
120C2×C4×D17—44no—
121C2×C4×D17—44no—
122C2×C4×D17—44no—
123C2×C4×D17C4211yescharacteristic
124C2×C4×D17C4211yescharacteristic
125C2×C4×D17C22⋊C411yescharacteristic
126C2×C4×D17C22⋊C411yescharacteristic
127C2×C4×D17C22⋊C411yescharacteristic
128C2×C4×D17C22⋊C411yescharacteristic
129C2×C4×D17C4⋊C411yescharacteristic
130C2×C4×D17C4⋊C411yescharacteristic
131C2×C4×D17C4⋊C411yescharacteristic
132C2×C4×D17C4⋊C411yescharacteristic
133C2×C4×D17C4⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C22×C411yescharacteristic
136C2×C4×D17C22×C411yescharacteristic
137C2×C4×D17C2×D411yescharacteristic
138C2×C4×D17C2×Q811yescharacteristic
139C22⋊#595—44no—
140C22⋊#595—42no—
141C22⋊#595—42no—
142C2×#3624—24no—
143C2×#3624—44no—
144C4⋊#595—44no—
145C4⋊#595—44no—
146#63242—44no—
147#63242—44no—
148C4⋊C4×C17—42no—
149C22⋊C4×C17—42no—
150C22⋊Dic17—42no—
151#63227—42no—
152#63227—42no—
153C4⋊Dic17—42no—
154#63225—44no—
155C2×#1289—171nomaximal, Sylow
156C23×C17—41no—
157C23×C17—41no—
158C23×C17#9511yescharacteristic
159C23×C17#9511yescharacteristic
160C23×C17#10212yes—
161C23×C17#10312yes—
162C23×C17C2×C22⋊C411yescharacteristic
163C22×D17—22no—
164C22×D17—22no—
165C22×D17—22no—
166C22×D17—22no—
167C22×D17—22no—
168C22×D17—22no—
169C22×D17—44no—
170C22×D17—44no—
171C22×D17—44no—
172C22×D17—44no—
173C22×D17—41no—
174C22×D17—41no—
175C22×D17—41no—
176C22×D17—41no—
177C22×D17—41no—
178C22×D17—41no—
179C22×D17#9511yescharacteristic
180C22×D17#9511yescharacteristic
181C22×D17#10212yes—
182C22×D17#10212yes—
183C22×D17#10212yes—
184C22×D17#10312yes—
185C22×D17#10312yes—
186C22×D17#10312yes—
187C22×D17#10612yes—
188C22×D17#10612yes—
189C22×D17#10712yes—
190C22×D17#10712yes—
191C22×D17C2×C22⋊C411yescharacteristic
192C22×D17C2×C4⋊C411yescharacteristic
193C22×D17C2×D811yescharacteristic
194C22×D17C2×SD1611yescharacteristic
195C22×D17C2×SD1611yescharacteristic
196C22×D17C2×Q1611yescharacteristic
197C2×#595—44no—
198C2×#595—44no—
199C2×#595—44no—
200C2×#595—88no—
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—41no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17—42no—
208C2×C4×C17—42no—
209C2×C4×C17—42no—
210C2×C4×C17#9511yescharacteristic
211C2×C4×C17#9511yescharacteristic
212C2×C4×C17C2×C4211yescharacteristic
213C2×C4×C17C2×C4⋊C411yescharacteristic
214C2×Dic17—22no—
215C2×Dic17—22no—
216C2×Dic17—22no—
217C2×Dic17—41no—
218C2×Dic17—41no—
219C2×Dic17—41no—
220C2×Dic17—42no—
221C2×Dic17—42no—
222C2×Dic17—42no—
223C2×Dic17#9511yescharacteristic
224C2×Dic17#9511yescharacteristic
225C2×Dic17C2×C22⋊C411yescharacteristic
226C2×Dic17C2×C4⋊C411yescharacteristic
227C4×D17—22no—
228C4×D17—22no—
229C4×D17—22no—
230C4×D17—22no—
231C4×D17—22no—
232C4×D17—22no—
233C4×D17—22no—
234C4×D17—22no—
235C4×D17—22no—
236C4×D17—41no—
237C4×D17—41no—
238C4×D17—41no—
239C4×D17—41no—
240C4×D17—41no—
241C4×D17—41no—
242C4×D17—88no—
243C4×D17#9914yes—
244#3624—44no—
245C22×C22⋊C8—171no—
246C2×#380—171no—
247C2×#380—171no—
248#1289—174no—
249C22×C17—21no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—21no—
253C22×C17—21no—
254C22×C17—21no—
255C22×C17—42no—
256C22×C17—42no—
257C22×C17#34012yes—
258C22×C17#34012yes—
259C22×C17C2×#9511yescharacteristic
260C22×C17C2×#10211yescharacteristic
261C22×C17C2×#10311yescharacteristic
262C2×D17—21no—
263C2×D17—21no—
264C2×D17—21no—
265C2×D17—21no—
266C2×D17—21no—
267C2×D17—21no—
268C2×D17—24no—
269C2×D17—24no—
270C2×D17—24no—
271C2×D17—24no—
272C2×D17—24no—
273C2×D17—24no—
274C2×D17—42no—
275C2×D17—42no—
276C2×D17—42no—
277C2×D17—42no—
278C2×D17—41no—
279C2×D17—41no—
280C2×D17—41no—
281C2×D17—41no—
282C2×D17H(3,ℤ/4)12yes—
283C2×D17#34012yes—
284C2×D17#34012yes—
285C2×D17#34212yes—
286C2×D17C2×#10211yescharacteristic
287C2×D17C2×#10311yescharacteristic
288C2×D17C2×#10611yescharacteristic
289C2×D17C2×#10711yescharacteristic
290#595—84no—
291C4×C17—21no—
292C4×C17—21no—
293C4×C17—21no—
294C4×C17—82no—
295C4×C17#34212yes—
296Dic17—21no—
297Dic17—21no—
298Dic17—21no—
299Dic17—82no—
300Dic17C2×#9912yes—
301C24×C4—171no—
302C23×C8—172no—
303C22×C4⋊C4—341no—
304C22×C4⋊C4—341no—
305C22×C22⋊C4—341no—
306C22×C22⋊C4—341no—
307C2×C22⋊C8—172no—
308C2×C22⋊C8—172no—
309C2×C22⋊C8—341no—
310C2×C22⋊C8—341no—
311C2×C22⋊C8—341no—
312C2×C22⋊C8—341no—
313#380—172no—
314#380—172no—
315#380—171no—
316#380—172no—
317#380—341no—
318#380—341no—
319#380—341no—
320#380—341no—
321#380#59511yescharacteristic, complemented
322C2×#95—172no—
323C2×#95—172no—
324C2×C17—21no—
325C2×C17—22no—
326C2×C17—22no—
327C2×C17—21no—
328C2×C17C2×H(3,ℤ/4)11yescharacteristic
329C2×C17C2×#34011yescharacteristic
330C2×C17C2×#34211yescharacteristic
331D17—21no—
332D17—22no—
333D17—21no—
334D17—21no—
335D17—21no—
336D17#128914yescomplemented
337C25—171no—
338C23×C4—171no—
339C23×C4—171no—
340C23×C4—171no—
341C23×C4—171no—
342C23×C4—171no—
343C23×C4—171no—
344C23×C4—171no—
345C23×C4—171no—
346C23×C4—171no—
347C23×C4—171no—
348C23×C4—171no—
349C23×C4—171no—
350C23×C4—171no—
351C23×C4—342no—
352C23×C4—342no—
353C23×C4—684no—
354C23×C4C2×#59511yescharacteristic
355C22×C8—174no—
356C22×C8—342no—
357C22×C8—342no—
358C22×C8—684no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—342no—
361C2×C4⋊C4—342no—
362C2×C4⋊C4—342no—
363C2×C4⋊C4—341no—
364C2×C4⋊C4—684no—
365C2×C4⋊C4—684no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—342no—
368C2×C22⋊C4—342no—
369C2×C22⋊C4—342no—
370C2×C22⋊C4—341no—
371C2×C22⋊C4—682no—
372C2×C22⋊C4—682no—
373C2×C22⋊C4—682no—
374C2×C22⋊C4—682no—
375C22⋊C8—342no—
376C22⋊C8—342no—
377C22⋊C8—342no—
378C22⋊C8—342no—
379#95—174no—
380#95—172no—
381#95—342no—
382#95—342no—
383#95C2×#59512yescomplemented
384C17C2×#128911yescharacteristic, complemented, Sylow
385C24—171no—
386C24—171no—
387C24—171no—
388C24—171no—
389C24—171no—
390C24—171no—
391C24—172no—
392C24—172no—
393C24—172no—
394C24—172no—
395C24—682no—
396C24—682no—
397C24C22⋊#59511yescharacteristic
398C22×C4—22no—
399C22×C4—42no—
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—171no—
414C22×C4—171no—
415C22×C4—171no—
416C22×C4—171no—
417C22×C4—171no—
418C22×C4—171no—
419C22×C4—171no—
420C22×C4—171no—
421C22×C4—171no—
422C22×C4—344no—
423C22×C4—344no—
424C22×C4—344no—
425C22×C4—344no—
426C22×C4—342no—
427C22×C4—682no—
428C22×C4—682no—
429C22×C4—682no—
430C22×C4—682no—
431C22×C4—682no—
432C22×C4—682no—
433C22×C4—682no—
434C22×C4—682no—
435C22×C4—682no—
436C22×C4—684no—
437C22×C4—684no—
438C22×C4—684no—
439C22×C4—682no—
440C22×C4—684no—
441C22×C4—684no—
442C22×C4—684no—
443C22×C4C4×#59511yescharacteristic
444C22×C4C4×#59511yescharacteristic
445C22×C4C4⋊#59511yescharacteristic
446C22×C4C4⋊#59511yescharacteristic
447C22×C4C22⋊#59511yescharacteristic
448C22×C4C22×#59511yescharacteristic
449C2×C8—344no—
450C2×C8—684no—
451C2×C8—684no—
452C2×C8—684no—
453C4⋊C4—42no—
454C4⋊C4—682no—
455C4⋊C4—684no—
456C4⋊C4—684no—
457C4⋊C4—684no—
458C22⋊C4—42no—
459C22⋊C4—682no—
460C22⋊C4—682no—
461C22⋊C4—682no—
462C22⋊C4—682no—
463C22⋊C4—684no—
464C22⋊C4—682no—
465C23—41no—
466C23—41no—
467C23—171no—
468C23—171no—
469C23—171no—
470C23—171no—
471C23—172no—
472C23—172no—
473C23—172no—
474C23—172no—
475C23—172no—
476C23—172no—
477C23—171no—
478C23—171no—
479C23—171no—
480C23—171no—
481C23—172no—
482C23—172no—
483C23—172no—
484C23—172no—
485C23—342no—
486C23—342no—
487C23—342no—
488C23—342no—
489C23—342no—
490C23—342no—
491C23—681no—
492C23—681no—
493C23—681no—
494C23—681no—
495C23—681no—
496C23—681no—
497C23—684no—
498C23—684no—
499C23—684no—
500C23—684no—
501C23(C2×#595)⋊C411yescharacteristic
502C23(C2×#595)⋊C411yescharacteristic
503C23#1058754712yes—
504C23#1058754912yes—
505C23C2×C22⋊#59511yescharacteristic
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—171no—
516C2×C4—174no—
517C2×C4—171no—
518C2×C4—171no—
519C2×C4—171no—
520C2×C4—342no—
521C2×C4—342no—
522C2×C4—342no—
523C2×C4—342no—
524C2×C4—342no—
525C2×C4—342no—
526C2×C4—342no—
527C2×C4—342no—
528C2×C4—342no—
529C2×C4—342no—
530C2×C4—342no—
531C2×C4—342no—
532C2×C4—681no—
533C2×C4—681no—
534C2×C4—681no—
535C2×C4—681no—
536C2×C4—681no—
537C2×C4—681no—
538C2×C4—681no—
539C2×C4—681no—
540C2×C4—681no—
541C2×C4—682no—
542C2×C4—682no—
543C2×C4—684no—
544C2×C4—684no—
545C2×C4—684no—
546C2×C4—682no—
547C2×C4—1368no—
548C2×C4—1368no—
549C2×C4(C2×#595)⋊C411yescharacteristic
550C2×C4(C2×#595)⋊C411yescharacteristic
551C2×C4C2×C4×#59511yescharacteristic
552C2×C4C2×C4⋊#59511yescharacteristic
553C8—684no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—42no—
561C22—42no—
562C22—172no—
563C22—172no—
564C22—172no—
565C22—171no—
566C22—172no—
567C22—171no—
568C22—171no—
569C22—171no—
570C22—344no—
571C22—344no—
572C22—344no—
573C22—344no—
574C22—344no—
575C22—344no—
576C22—341no—
577C22—341no—
578C22—341no—
579C22—341no—
580C22—341no—
581C22—341no—
582C22—681no—
583C22—681no—
584C22—681no—
585C22—681no—
586C22—682no—
587C22—682no—
588C22—682no—
589C22—682no—
590C22#1176368212yes—
591C22#1176368212yes—
592C22C2×(C2×#595)⋊C411yescharacteristic
593C22C2×#1058754711yescharacteristic
594C22C2×#1058754911yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—82no—
599C4—172no—
600C4—341no—
601C4—341no—
602C4—341no—
603C4—1362no—
604C4—1364no—
605C4#1176368612yes—
606C2—21no—
607C2—21no—
608C2—22no—
609C2—22no—
610C2—174no—
611C2—341no—
612C2—342no—
613C2—341no—
614C2—341no—
615C2—341no—
616C2#1454445411yescharacteristic
617C2C2×#1176368211yescharacteristic
618C2C2×#1176368611yescharacteristic
subgroupG/H
centerC22C2×(C2×#595)⋊C4
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC22×C17C2×#95
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenter#380#595
hypocenterC17C2×#1289
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543646C2semidirect
5. C22×#63242C4semidirect
11. #11763777C4semidirect
16. #11763751C4semidirect
18. C2×(C2×#595)⋊C4C4semidirect
22. #11762669C4semidirect
26. #95×D17C4semidirect
27. C17×#380C4semidirect
56. C2×#63242C2×C4semidirect
69. (C2×#595)⋊C4C2×C4semidirect
72. C17×#95C2×C4semidirect
74. #10587502C2×C4semidirect
321. #380#595semidirect
336. D17#1289semidirect
383. #95C2×#595semidirect
384. C17C2×#1289semidirect

Maximal subgroups

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

subgroupindex
C2×#117637772
C2×#117637512
#145436462
D17×#3802
C2×#128917