Finite Group Databasebeta

← #17950639

Subgroups — #17950639

Order 4352.

954 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17⋊#407C211yesmaximal, characteristic
2#14545228C211yesmaximal, characteristic
3#14543626C214yesmaximal, complemented
4C22×#10587491C211yesmaximal, characteristic
5C2×D17⋊M16—21no—
6C2×#10587677—21no—
7#11763781—21no—
8#11763780—21no—
9#11763780C412yescomplemented
10#11763779C412yescomplemented
11#11763777—21no—
12#11763777C2212yes—
13#11763752—21no—
14#11763751—21no—
15#11763751C412yes—
16#11763750C412yes—
17C4×C22⋊#595—21no—
18C4×C22⋊#595C2212yes—
19C23×C4×D17C2211yescharacteristic
20C23×#3622C411yescharacteristic, complemented
21C2×#10587491—21no—
22C2×#10587491—21no—
23C2×#10587491—21no—
24C2×#10587491—21no—
25C2×#10587491C412yescomplemented
26C2×#10587491C2212yes—
27C23×C8×C17C411yescharacteristic, complemented
28C24×D17C2×C411yescharacteristic
29C23×C4×C17C2×C411yescharacteristic
30C23×Dic17C2×C411yescharacteristic
31C22×C4×D17—42no—
32C22×C4×D17—42no—
33C22×C4×D17C2×C411yescharacteristic
34C22×C4×D17C2×C411yescharacteristic
35C22×C4×D17C2×C411yescharacteristic
36C22×C4×D17D411yescharacteristic
37C22×C4×D17D411yescharacteristic
38C22×C4×D17D411yescharacteristic
39C22×C4×D17D411yescharacteristic
40C22×C4×D17D411yescharacteristic
41C22×C4×D17D411yescharacteristic
42C22×C4×D17Q811yescharacteristic
43C22×C4×D17Q811yescharacteristic
44C22×C4×D17C2311yescharacteristic
45C2×C22⋊#595—22no—
46C2×C22⋊#595—22no—
47C2×C22⋊#595C2×C414yes—
48C2×#63247—22no—
49#10587677—42no—
50#10587677—42no—
51C2×C4⋊#595—22no—
52C2×C4×#595—22no—
53D17⋊M16—42no—
54D17⋊M16—42no—
55C2×#63243—22no—
56C2×#63242—22no—
57C22×C8×C17—21no—
58C22×C8×C17—21no—
59C22×C8×C17—42no—
60C22×C8×C17C2×C412yes—
61C22×#3622—21no—
62C22×#3622—21no—
63C22×#3622—42no—
64C22×#3622C2×C412yes—
65C22⋊#3624—22no—
66C22⋊#3624C2×C414yes—
67(C2×#595)⋊C4—22no—
68(C2×#595)⋊C4—22no—
69#10587543—22no—
70#10587543—22no—
71#10587491—22no—
72#10587491—22no—
73#10587491—22no—
74#10587491—22no—
75C24×C17C4211yescharacteristic
76C23×D17—24no—
77C23×D17—42no—
78C23×D17—42no—
79C23×D17C4211yescharacteristic
80C23×D17C22⋊C411yescharacteristic
81C23×D17C22⋊C411yescharacteristic
82C23×D17C4⋊C411yescharacteristic
83C23×D17C4⋊C411yescharacteristic
84C23×D17C22×C411yescharacteristic
85C22×#595—24no—
86C22×C4×C17—22no—
87C22×C4×C17—22no—
88C22×C4×C17C4211yescharacteristic
89C22×C4×C17C22⋊C411yescharacteristic
90C22×C4×C17C22⋊C411yescharacteristic
91C22×C4×C17C4⋊C411yescharacteristic
92C22×C4×C17C4⋊C411yescharacteristic
93C22×C4×C17C22×C411yescharacteristic
94C22×Dic17—42no—
95C22×Dic17C4211yescharacteristic
96C22×Dic17C22⋊C411yescharacteristic
97C22×Dic17C22⋊C411yescharacteristic
98C22×Dic17C4⋊C411yescharacteristic
99C22×Dic17C4⋊C411yescharacteristic
100C22×Dic17C22×C411yescharacteristic
101C2×C4×D17—22no—
102C2×C4×D17—22no—
103C2×C4×D17—22no—
104C2×C4×D17—22no—
105C2×C4×D17—42no—
106C2×C4×D17—42no—
107C2×C4×D17—41no—
108C2×C4×D17—41no—
109C2×C4×D17—42no—
110C2×C4×D17—41no—
111C2×C4×D17—41no—
112C2×C4×D17—41no—
113C2×C4×D17—41no—
114C2×C4×D17—42no—
115C2×C4×D17—41no—
116C2×C4×D17—41no—
117C2×C4×D17—42no—
118C2×C4×D17—42no—
119C2×C4×D17C22⋊C411yescharacteristic
120C2×C4×D17C22⋊C411yescharacteristic
121C2×C4×D17C22⋊C411yescharacteristic
122C2×C4×D17C22⋊C411yescharacteristic
123C2×C4×D17C22⋊C411yescharacteristic
124C2×C4×D17C22⋊C411yescharacteristic
125C2×C4×D17C4⋊C411yescharacteristic
126C2×C4×D17C4⋊C411yescharacteristic
127C2×C4×D17C4⋊C411yescharacteristic
128C2×C4×D17C4⋊C411yescharacteristic
129C2×C4×D17C4⋊C411yescharacteristic
130C2×C4×D17C4⋊C411yescharacteristic
131C2×C4×D17C2×D411yescharacteristic
132C2×C4×D17C2×D411yescharacteristic
133C2×C4×D17C2×D411yescharacteristic
134C2×C4×D17C2×Q811yescharacteristic
135C22⋊#595—28no—
136C22⋊#595—44no—
137C22⋊#595—44no—
138#63247—44no—
139C2×#3624—24no—
140C4⋊#595—44no—
141C4×#595—42no—
142C4×#595—42no—
143#63243—44no—
144#63242—42no—
145#63242—42no—
146C2×C8×C17—22no—
147C2×C8×C17—42no—
148C2×C8×C17—42no—
149C2×C8×C17—42no—
150C2×#3622—22no—
151C2×#3622—42no—
152C2×#3622—42no—
153C2×#3622—42no—
154#7927—171nomaximal, Sylow
155C23×C17—22no—
156C23×C17—22no—
157C23×C17—22no—
158C23×C17#9511yescharacteristic
159C23×C17#9511yescharacteristic
160C23×C17C2×C4211yescharacteristic
161C22×D17—22no—
162C22×D17—22no—
163C22×D17—22no—
164C22×D17—22no—
165C22×D17—22no—
166C22×D17—22no—
167C22×D17—22no—
168C22×D17—22no—
169C22×D17—22no—
170C22×D17—41no—
171C22×D17—41no—
172C22×D17—41no—
173C22×D17—41no—
174C22×D17—41no—
175C22×D17—41no—
176C22×D17—41no—
177C22×D17—41no—
178C22×D17—416no—
179C22×D17#9511yescharacteristic
180C22×D17#9511yescharacteristic
181C22×D17C2×C22⋊C411yescharacteristic
182C22×D17C2×C4⋊C411yescharacteristic
183C22×D17#13114yes—
184C2×#595—44no—
185C2×#595—44no—
186C2×#595—44no—
187C2×C4×C17—22no—
188C2×C4×C17—22no—
189C2×C4×C17—22no—
190C2×C4×C17—21no—
191C2×C4×C17—21no—
192C2×C4×C17—21no—
193C2×C4×C17—21no—
194C2×C4×C17#9511yescharacteristic
195C2×C4×C17#9511yescharacteristic
196C2×C4×C17#9912yes—
197C2×C4×C17#9912yes—
198C2×C4×C17C2×C22⋊C411yescharacteristic
199C2×C4×C17C2×C4⋊C411yescharacteristic
200C2×Dic17—22no—
201C2×Dic17—22no—
202C2×Dic17—41no—
203C2×Dic17—41no—
204C2×Dic17—41no—
205C2×Dic17—41no—
206C2×Dic17#9511yescharacteristic
207C2×Dic17#9511yescharacteristic
208C2×Dic17C2×C22⋊C411yescharacteristic
209C2×Dic17C2×C4⋊C411yescharacteristic
210C4×D17—22no—
211C4×D17—22no—
212C4×D17—22no—
213C4×D17—22no—
214C4×D17—21no—
215C4×D17—21no—
216C4×D17—21no—
217C4×D17—21no—
218C4×D17—21no—
219C4×D17—21no—
220C4×D17—21no—
221C4×D17—21no—
222C4×D17—41no—
223C4×D17—41no—
224C4×D17—41no—
225C4×D17—41no—
226C4×D17—41no—
227C4×D17—41no—
228C4×D17—41no—
229C4×D17—41no—
230#3624—44no—
231C8×C17—42no—
232#3622—42no—
233C2×#407—171no—
234C22×C22⋊C8—171no—
235#2280—171no—
236#1282—174no—
237C22×C17—28no—
238C22×C17—21no—
239C22×C17—21no—
240C22×C17—21no—
241C22×C17—21no—
242C22×C17—21no—
243C22×C17—21no—
244C22×C17#34212yes—
245C22×C17#34412yes—
246C22×C17C2×#9511yescharacteristic
247C22×C17#40512yes—
248C2×D17—21no—
249C2×D17—21no—
250C2×D17—21no—
251C2×D17—21no—
252C2×D17—21no—
253C2×D17—21no—
254C2×D17—21no—
255C2×D17—21no—
256C2×D17—21no—
257C2×D17—21no—
258C2×D17—44no—
259C2×D17—44no—
260C2×D17—44no—
261C2×D17—44no—
262C2×D17—44no—
263C2×D17—44no—
264C2×D17#40812yes—
265C2×D17#42412yes—
266#595—84no—
267C4×C17—21no—
268C4×C17—21no—
269C4×C17#34212yes—
270C4×C17C2×#9911yescharacteristic
271C4×C17C2×#9911yescharacteristic
272Dic17—21no—
273Dic17—21no—
274Dic17—21no—
275Dic17—21no—
276C24×C4—171no—
277C22×M16—341no—
278C23×C8—171no—
279C23×C8#59511yescharacteristic, complemented
280C2×#117—341no—
281#407—172no—
282#407—172no—
283#407—341no—
284#407—341no—
285C2×C22⋊C8—172no—
286C2×C22⋊C8—172no—
287C2×C22⋊C8—172no—
288C2×C22⋊C8—341no—
289C2×C22⋊C8—341no—
290C2×C22⋊C8—341no—
291C2×C22⋊C8—341no—
292C2×C22⋊C8—341no—
293#381—341no—
294#380—172no—
295#380—341no—
296#379—172no—
297C4×C22⋊C4—172no—
298C4×C22⋊C4—341no—
299C2×C17—22no—
300C2×C17—22no—
301C2×C17—22no—
302C2×C17#172911yescharacteristic
303C2×C17C2×#34211yescharacteristic
304C2×C17C2×#34411yescharacteristic
305D17—22no—
306D17—22no—
307D17—41no—
308D17—41no—
309C25—171no—
310C23×C4—171no—
311C23×C4—171no—
312C23×C4—171no—
313C23×C4—171no—
314C23×C4—171no—
315C23×C4—171no—
316C23×C4—171no—
317C23×C4—171no—
318C23×C4—171no—
319C23×C4—171no—
320C23×C4—171no—
321C23×C4—171no—
322C23×C4—171no—
323C23×C4—682no—
324C23×C4—682no—
325C23×C4C2×#59511yescharacteristic
326C2×M16—342no—
327C2×M16—342no—
328C2×M16—682no—
329C2×M16—682no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—42no—
333C22×C8—172no—
334C22×C8—342no—
335C22×C8—341no—
336C22×C8—341no—
337C22×C8—682no—
338C22×C8C2×#59512yes—
339#117—682no—
340#117—682no—
341C2×C4⋊C4—342no—
342C2×C22⋊C4—174no—
343C2×C22⋊C4—342no—
344C2×C22⋊C4—342no—
345C2×C42—342no—
346C22⋊C8—174no—
347C22⋊C8—342no—
348C22⋊C8—342no—
349C22⋊C8—342no—
350C22⋊C8—342no—
351C22⋊C8—342no—
352C22⋊C8—342no—
353C22⋊C8—342no—
354#95—342no—
355#95—342no—
356C17#792711yescharacteristic, complemented, Sylow
357C24—171no—
358C24—171no—
359C24—171no—
360C24—171no—
361C24—171no—
362C24—171no—
363C24—344no—
364C24—682no—
365C24—682no—
366C24C4×#59511yescharacteristic
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—171no—
370C22×C4—171no—
371C22×C4—171no—
372C22×C4—171no—
373C22×C4—171no—
374C22×C4—171no—
375C22×C4—171no—
376C22×C4—171no—
377C22×C4—171no—
378C22×C4—171no—
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—342no—
392C22×C4—342no—
393C22×C4—342no—
394C22×C4—342no—
395C22×C4—344no—
396C22×C4—681no—
397C22×C4—681no—
398C22×C4—681no—
399C22×C4—681no—
400C22×C4—681no—
401C22×C4—681no—
402C22×C4—681no—
403C22×C4—681no—
404C22×C4—682no—
405C22×C4—682no—
406C22×C4—682no—
407C22×C4—682no—
408C22×C4—682no—
409C22×C4—682no—
410C22×C4—682no—
411C22×C4C4×#59511yescharacteristic
412C22×C4C4⋊#59511yescharacteristic
413C22×C4C4⋊#59511yescharacteristic
414C22×C4C22⋊#59511yescharacteristic
415C22×C4C22⋊#59511yescharacteristic
416C22×C4C22×#59511yescharacteristic
417M16—684no—
418M16—684no—
419C2×C8—22no—
420C2×C8—42no—
421C2×C8—42no—
422C2×C8—42no—
423C2×C8—344no—
424C2×C8—342no—
425C2×C8—682no—
426C2×C8—682no—
427C2×C8—682no—
428C2×C8—682no—
429C2×C8—682no—
430C4⋊C4—684no—
431C22⋊C4—348no—
432C22⋊C4—684no—
433C22⋊C4—684no—
434C42—682no—
435C42—682no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—171no—
440C23—171no—
441C23—174no—
442C23—171no—
443C23—171no—
444C23—342no—
445C23—342no—
446C23—342no—
447C23—342no—
448C23—342no—
449C23—342no—
450C23—342no—
451C23—342no—
452C23—342no—
453C23—681no—
454C23—681no—
455C23—681no—
456C23—681no—
457C23—681no—
458C23—681no—
459C23—681no—
460C23—681no—
461C23—6816no—
462C23(C2×#595)⋊C411yescharacteristic
463C23(C2×#595)⋊C411yescharacteristic
464C23C2×C4×#59511yescharacteristic
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—171no—
473C2×C4—171no—
474C2×C4—171no—
475C2×C4—171no—
476C2×C4—342no—
477C2×C4—342no—
478C2×C4—341no—
479C2×C4—341no—
480C2×C4—341no—
481C2×C4—341no—
482C2×C4—341no—
483C2×C4—341no—
484C2×C4—341no—
485C2×C4—341no—
486C2×C4—342no—
487C2×C4—342no—
488C2×C4—342no—
489C2×C4—342no—
490C2×C4—681no—
491C2×C4—681no—
492C2×C4—681no—
493C2×C4—681no—
494C2×C4—681no—
495C2×C4—681no—
496C2×C4—681no—
497C2×C4—681no—
498C2×C4—681no—
499C2×C4—681no—
500C2×C4—681no—
501C2×C4—681no—
502C2×C4—684no—
503C2×C4—684no—
504C2×C4—684no—
505C2×C4#1058753912yes—
506C2×C4(C2×#595)⋊C411yescharacteristic
507C2×C4(C2×#595)⋊C411yescharacteristic
508C2×C4#1058755112yes—
509C2×C4C2×C4⋊#59511yescharacteristic
510C2×C4C2×C22⋊#59511yescharacteristic
511C8—42no—
512C8—684no—
513C8—682no—
514C22—28no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—172no—
522C22—172no—
523C22—341no—
524C22—341no—
525C22—341no—
526C22—341no—
527C22—341no—
528C22—341no—
529C22—341no—
530C22—341no—
531C22—341no—
532C22—341no—
533C22—684no—
534C22—684no—
535C22—684no—
536C22—684no—
537C22—684no—
538C22—684no—
539C22#1176368712yes—
540C22#1176369112yes—
541C22C2×(C2×#595)⋊C411yescharacteristic
542C22#1176377212yes—
543C4—21no—
544C4—21no—
545C4—341no—
546C4—341no—
547C4—341no—
548C4—341no—
549C4—1364no—
550C4#1176368712yes—
551C4C2×#1058755111yescharacteristic
552C4C2×#1058753911yescharacteristic
553C2—22no—
554C2—22no—
555C2—22no—
556C2—342no—
557C2—342no—
558C2—681no—
559C2—681no—
560C2#1454444911yescharacteristic
561C2C2×#1176368711yescharacteristic
562C2C2×#1176369111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC23×C17C2×C42
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC22×C17C2×#95
prime radicalC24×D17C2×C4
cosocleC22×C4×D17C23
hypercenterC23×C8#595
hypocenterC17#7927
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
3. #14543626C2semidirect
9. #11763780C4semidirect
10. #11763779C4semidirect
20. C23×#3622C4semidirect
25. C2×#10587491C4semidirect
27. C23×C8×C17C4semidirect
279. C23×C8#595semidirect
356. C17#7927semidirect

Maximal subgroups

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

subgroupindex
D17⋊#4072
#145452282
#145436262
C22×#105874912
#792717